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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 112710.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.cz1 | 112710dc1 | \([1, 0, 0, -2949540, 1949997492]\) | \(-406813373046721/118462500\) | \(-826365665854462500\) | \([]\) | \(3231360\) | \(2.4175\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 112710.cz1 has rank \(1\).
Complex multiplication
The elliptic curves in class 112710.cz do not have complex multiplication.Modular form 112710.2.a.cz
sage: E.q_eigenform(10)