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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 193600fn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.d1 | 193600fn1 | \([0, 0, 0, 60500, -6050000]\) | \(3267/4\) | \(-29984768000000000\) | \([]\) | \(2396160\) | \(1.8477\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193600fn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 193600fn do not have complex multiplication.Modular form 193600.2.a.fn
sage: E.q_eigenform(10)