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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 212160.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.cr1 | 212160cl1 | \([0, -1, 0, -2605, -81725]\) | \(-30558612127744/28361896875\) | \(-1815161400000\) | \([]\) | \(259200\) | \(1.0488\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 212160.cr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 212160.cr do not have complex multiplication.Modular form 212160.2.a.cr
sage: E.q_eigenform(10)