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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 137904.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
137904.j1 | 137904cw1 | \([0, -1, 0, -166521, 26241669]\) | \(-69842532158464/96702579\) | \(-707052123857664\) | \([]\) | \(684288\) | \(1.7536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 137904.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 137904.j do not have complex multiplication.Modular form 137904.2.a.j
sage: E.q_eigenform(10)