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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 106722.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.c1 | 106722d1 | \([1, -1, 0, -9917364, -12080145456]\) | \(-705703720113/4194304\) | \(-641135751838121852928\) | \([]\) | \(10872576\) | \(2.8326\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 106722.c do not have complex multiplication.Modular form 106722.2.a.c
sage: E.q_eigenform(10)