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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1682.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1682.j1 | 1682g1 | \([1, -1, 1, -999, 17779]\) | \(-185193/116\) | \(-68999505236\) | \([]\) | \(3360\) | \(0.78142\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1682.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1682.j do not have complex multiplication.Modular form 1682.2.a.j
sage: E.q_eigenform(10)