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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 121242r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121242.e1 | 121242r1 | \([1, 0, 1, -3456610, 2433177140]\) | \(2578211650978275313/47984989814784\) | \(85008336541268557824\) | \([]\) | \(6289920\) | \(2.6183\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121242r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 121242r do not have complex multiplication.Modular form 121242.2.a.r
sage: E.q_eigenform(10)