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SageMath
E = EllipticCurve("lm1")
E.isogeny_class()
Elliptic curves in class 487872.lm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.lm1 | 487872lm1 | \([0, 0, 0, -9372, 378488]\) | \(-91625216/9261\) | \(-9201601575936\) | \([]\) | \(884736\) | \(1.2275\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872.lm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 487872.lm do not have complex multiplication.Modular form 487872.2.a.lm
sage: E.q_eigenform(10)