Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 409101d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 409101.d1 | 409101d1 | \([0, 1, 1, -962474, -10275428740]\) | \(-473093337088/218558899251\) | \(-45552565971525379413339\) | \([]\) | \(44236800\) | \(3.0269\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 409101d do not have complex multiplication.Modular form 409101.2.a.d
sage: E.q_eigenform(10)