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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 13872f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13872.l1 | 13872f1 | \([0, -1, 0, -4720, -123296]\) | \(-68001122/27\) | \(-4618377216\) | \([]\) | \(12960\) | \(0.81853\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 13872f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 13872f do not have complex multiplication.Modular form 13872.2.a.f
sage: E.q_eigenform(10)