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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 3675.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3675.p1 | 3675m1 | \([0, 1, 1, -380158, -148802531]\) | \(-1376628736/1366875\) | \(-6032943062138671875\) | \([]\) | \(112896\) | \(2.2994\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3675.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 3675.p do not have complex multiplication.Modular form 3675.2.a.p
sage: E.q_eigenform(10)