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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 10002a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10002.c1 | 10002a1 | \([1, 1, 0, -1804, 32080]\) | \(-649844448647113/89597435904\) | \(-89597435904\) | \([]\) | \(14560\) | \(0.83330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10002a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10002a do not have complex multiplication.Modular form 10002.2.a.a
sage: E.q_eigenform(10)