Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 817a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
817.a1 | 817a1 | \([0, 1, 1, 1, 6]\) | \(32768/15523\) | \(-15523\) | \([]\) | \(56\) | \(-0.51674\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 817a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 817a do not have complex multiplication.Modular form 817.2.a.a
sage: E.q_eigenform(10)