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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 75712.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75712.bd1 | 75712be1 | \([0, -1, 0, -49845761, 135707039233]\) | \(-10824513276632329/21926008832\) | \(-27743395974840867356672\) | \([]\) | \(9934848\) | \(3.1934\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.bd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75712.bd do not have complex multiplication.Modular form 75712.2.a.bd
sage: E.q_eigenform(10)