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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 40310m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40310.f1 | 40310m1 | \([1, 1, 0, -322, -3916]\) | \(-3710197529641/4031000000\) | \(-4031000000\) | \([]\) | \(27648\) | \(0.53792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40310m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40310m do not have complex multiplication.Modular form 40310.2.a.m
sage: E.q_eigenform(10)