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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 400192.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400192.bf1 | 400192bf1 | \([0, 1, 0, -6309, 172355]\) | \(351232/37\) | \(2926050230272\) | \([]\) | \(491520\) | \(1.1268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 400192.bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 400192.bf do not have complex multiplication.Modular form 400192.2.a.bf
sage: E.q_eigenform(10)