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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 88445.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88445.bg1 | 88445f1 | \([1, 0, 1, -654670259, -6447317053943]\) | \(877952898529/15625\) | \(552255888969335353140625\) | \([]\) | \(26199936\) | \(3.6829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 88445.bg1 has rank \(0\).
Complex multiplication
The elliptic curves in class 88445.bg do not have complex multiplication.Modular form 88445.2.a.bg
sage: E.q_eigenform(10)