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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 440818bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 440818.bd1 | 440818bd1 | \([1, 1, 1, 718058953, -96723142259]\) | \(21847267201615503339679487/12645264248262093704704\) | \(-23699261088787133799701753344\) | \([]\) | \(463656960\) | \(4.1341\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 440818bd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 440818bd do not have complex multiplication.Modular form 440818.2.a.bd
sage: E.q_eigenform(10)