A332545 The j-invariants of the elliptic curves defined over Q with good reduction away from 2.

128, 1728, 8000, 10976, 287496

Offset: 1

Author

N. J. A. Sloane, Feb 19 2020

Keywords

• nonn
• fini
• full

Examples

			From _Robin Visser_, Nov 26 2023: (Start)
There are exactly 24 isomorphism classes of elliptic curves defined over Q with good reduction away from 2, classified by Ogg (1966).
There are 4 curves with j-invariant 128 given by y^2 = x^3 + x^2 + x + 1, y^2 = x^3 + x^2 + 3x - 5, y^2 = x^3 - x^2 + x - 1, and y^2 = x^3 - x^2 + 3x + 5.
There are 8 curves with j-invariant 1728 given by y^2 = x^3 - x, y^2 = x^3 + 4x, y^2 = x^3 - 4x, y^2 = x^3 + x, y^2 = x^3 - 2x, y^2 = x^3 + 8x, y^2 = x^3 -8x, and y^2 = x^3 + 2x.
There are 4 curves with j-invariant 8000 given by y^2 = x^3 + x^2 - 13x - 21, y^2 = x^3 + x^2 - 3x + 1, y^2 = x^3 - x^2 - 13x + 21, and y^2 = x^3 - x^2 - 3x - 1.
There are 4 curves with j-invariant 10976 given by y^2 = x^3 + x^2 - 9x + 7, y^2 = x^3 + x^2 - 2x - 2, y^2 = x^3 - x^2 - 9x - 7, and y^2 = x^3 - x^2 - 2x + 2.
There are 4 curves with j-invariant 287496 given by y^2 = x^3 - 11x - 14, y^2 = x^3 - 11x + 14, y^2 = x^3 - 44x - 112, and y^2 = x^3 - 44x + 112. (End)
		

References

• Pinch, R. G. (1984, July). Elliptic curves with good reduction away from 2. Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 96, No. 1, pp. 25-38). Cambridge University Press. See Prop. 4.1.

Links

• A. P. Ogg, Abelian curves of 2-power conductor, Proc. Cambridge Philos. Soc. 62 (1966), 143-148.

Crossrefs

Cf. A359480.

Programs

Sage

set(E.j_invariant() for E in EllipticCurves_with_good_reduction_outside_S([2]))  # Robin Visser, Nov 26 2023