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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 272734j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272734.j1 | 272734j1 | \([1, 1, 0, -990266, 162401716]\) | \(25248276104737/11918987872\) | \(50697628990493168992\) | \([]\) | \(6912000\) | \(2.4752\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 272734j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 272734j do not have complex multiplication.Modular form 272734.2.a.j
sage: E.q_eigenform(10)