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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 67280r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67280.m1 | 67280r1 | \([0, 0, 0, -1381763, 625100162]\) | \(100709966211849/13107200\) | \(37971859551027200\) | \([]\) | \(766080\) | \(2.2018\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67280r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 67280r do not have complex multiplication.Modular form 67280.2.a.r
sage: E.q_eigenform(10)