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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 6240.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6240.f1 | 6240t1 | \([0, -1, 0, -541, -8555]\) | \(-4283098624/5569395\) | \(-22812241920\) | \([]\) | \(4480\) | \(0.68056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6240.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 6240.f do not have complex multiplication.Modular form 6240.2.a.f
sage: E.q_eigenform(10)