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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8372f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8372.d1 | 8372f1 | \([0, -1, 0, -85, 8513]\) | \(-268435456/121324931\) | \(-31059182336\) | \([]\) | \(4032\) | \(0.69238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8372f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8372f do not have complex multiplication.Modular form 8372.2.a.f
sage: E.q_eigenform(10)