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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 12138.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12138.k1 | 12138g1 | \([1, 0, 1, -4218684, -3343946630]\) | \(-344002044213921241/1011143540736\) | \(-24406546983419510784\) | \([]\) | \(587520\) | \(2.5904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12138.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12138.k do not have complex multiplication.Modular form 12138.2.a.k
sage: E.q_eigenform(10)