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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 187200.fr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.fr1 | 187200ds1 | \([0, 0, 0, -59700, -8820250]\) | \(-32278933504/27421875\) | \(-19990546875000000\) | \([]\) | \(1290240\) | \(1.8255\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 187200.fr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 187200.fr do not have complex multiplication.Modular form 187200.2.a.fr
sage: E.q_eigenform(10)