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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1740.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1740.g1 | 1740h1 | \([0, 1, 0, -190, 1025]\) | \(-47659369216/4404375\) | \(-70470000\) | \([]\) | \(480\) | \(0.24839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1740.g1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1740.g do not have complex multiplication.Modular form 1740.2.a.g
sage: E.q_eigenform(10)