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SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 69696.fw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69696.fw1 | 69696cf1 | \([0, 0, 0, 87846, 77626582]\) | \(61952/2187\) | \(-2646568486536967872\) | \([]\) | \(709632\) | \(2.2149\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69696.fw1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69696.fw do not have complex multiplication.Modular form 69696.2.a.fw
sage: E.q_eigenform(10)