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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 6690.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6690.e1 | 6690f1 | \([1, 0, 1, -2051948, 1692676778]\) | \(-955481890654443135203641/685056000000000000000\) | \(-685056000000000000000\) | \([]\) | \(405000\) | \(2.6978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6690.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 6690.e do not have complex multiplication.Modular form 6690.2.a.e
sage: E.q_eigenform(10)