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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 75504cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75504.co1 | 75504cz1 | \([0, 1, 0, -117, 867]\) | \(-360448/507\) | \(-251277312\) | \([]\) | \(27648\) | \(0.30412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75504cz1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75504cz do not have complex multiplication.Modular form 75504.2.a.cz
sage: E.q_eigenform(10)