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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 212160.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.r1 | 212160hj1 | \([0, -1, 0, 1149439, 1209726465]\) | \(640680045567719039/2783963520000000\) | \(-729799332986880000000\) | \([]\) | \(10063872\) | \(2.6858\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 212160.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 212160.r do not have complex multiplication.Modular form 212160.2.a.r
sage: E.q_eigenform(10)