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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 121680.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121680.j1 | 121680cn1 | \([0, 0, 0, 117, 442]\) | \(9477/10\) | \(-186900480\) | \([]\) | \(50688\) | \(0.27388\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121680.j1 has rank \(2\).
Complex multiplication
The elliptic curves in class 121680.j do not have complex multiplication.Modular form 121680.2.a.j
sage: E.q_eigenform(10)