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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 19600c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.bg1 | 19600c1 | \([0, -1, 0, -408, -2813]\) | \(12544\) | \(600250000\) | \([]\) | \(6720\) | \(0.42785\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19600c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19600c do not have complex multiplication.Modular form 19600.2.a.c
sage: E.q_eigenform(10)