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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1694j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1694.j1 | 1694j1 | \([1, -1, 1, -127194, -28630247]\) | \(-8773917273/8605184\) | \(-223196311177731584\) | \([]\) | \(47520\) | \(2.0248\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1694j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1694j do not have complex multiplication.Modular form 1694.2.a.j
sage: E.q_eigenform(10)