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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 121275x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121275.j1 | 121275x1 | \([0, 0, 1, -14586075, 21455711156]\) | \(-3950456832/3025\) | \(-262794999786760546875\) | \([]\) | \(10644480\) | \(2.8503\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121275x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 121275x do not have complex multiplication.Modular form 121275.2.a.x
sage: E.q_eigenform(10)