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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 77616bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.bc1 | 77616bd1 | \([0, 0, 0, -5891319, -5504284611]\) | \(-610325920583424/55240493\) | \(-2046713532510666096\) | \([]\) | \(2211840\) | \(2.5531\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77616bd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 77616bd do not have complex multiplication.Modular form 77616.2.a.bd
sage: E.q_eigenform(10)