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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 137904r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
137904.cx1 | 137904r1 | \([0, 1, 0, -11717, -1950285]\) | \(-53248/459\) | \(-1533625962246144\) | \([]\) | \(786240\) | \(1.5965\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 137904r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 137904r do not have complex multiplication.Modular form 137904.2.a.r
sage: E.q_eigenform(10)