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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 144400.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144400.f1 | 144400d1 | \([0, 1, 0, -192533, -32707937]\) | \(-4194304/19\) | \(-3575486956000000\) | \([]\) | \(1209600\) | \(1.8360\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 144400.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 144400.f do not have complex multiplication.Modular form 144400.2.a.f
sage: E.q_eigenform(10)