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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 388080.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.r1 | 388080r1 | \([0, 0, 0, -5119241043, 155869767626258]\) | \(-861923363555648023441/110929177533556800\) | \(-1909490884099695367739257651200\) | \([]\) | \(553512960\) | \(4.5439\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 388080.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 388080.r do not have complex multiplication.Modular form 388080.2.a.r
sage: E.q_eigenform(10)