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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 234416.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234416.r1 | 234416r1 | \([0, -1, 0, -1275045, -595731191]\) | \(-155337497706496/14140645571\) | \(-20868609978456670976\) | \([]\) | \(3931200\) | \(2.4500\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 234416.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 234416.r do not have complex multiplication.Modular form 234416.2.a.r
sage: E.q_eigenform(10)