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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1309.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1309.c1 | 1309a1 | \([0, 0, 1, -406957, -99924251]\) | \(-7453654902730081529856/45254746691\) | \(-45254746691\) | \([]\) | \(16128\) | \(1.6523\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1309.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1309.c do not have complex multiplication.Modular form 1309.2.a.c
sage: E.q_eigenform(10)