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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 12274k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12274.j1 | 12274k1 | \([1, -1, 1, 654, -1935]\) | \(237719583/147968\) | \(-19283337728\) | \([]\) | \(18144\) | \(0.66264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12274k1 has rank \(2\).
Complex multiplication
The elliptic curves in class 12274k do not have complex multiplication.Modular form 12274.2.a.k
sage: E.q_eigenform(10)