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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 85782.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85782.f1 | 85782e1 | \([1, 1, 0, -2962019, -1963438947]\) | \(-4831694578428193/184650192\) | \(-109834240428727632\) | \([]\) | \(2257920\) | \(2.3553\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 85782.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 85782.f do not have complex multiplication.Modular form 85782.2.a.f
sage: E.q_eigenform(10)