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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 121275.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121275.u1 | 121275et1 | \([0, 0, 1, -3675, 9464656]\) | \(-4096/28875\) | \(-38695261623046875\) | \([]\) | \(1327104\) | \(1.8618\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121275.u1 has rank \(2\).
Complex multiplication
The elliptic curves in class 121275.u do not have complex multiplication.Modular form 121275.2.a.u
sage: E.q_eigenform(10)