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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 19600cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.ee1 | 19600cz1 | \([0, 0, 0, -3521875, 2750431250]\) | \(-1026590625/100352\) | \(-472252497920000000000\) | \([]\) | \(1520640\) | \(2.7079\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19600cz1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19600cz do not have complex multiplication.Modular form 19600.2.a.cz
sage: E.q_eigenform(10)