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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 272734s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272734.s1 | 272734s1 | \([1, -1, 0, -197617646, 1069318441428]\) | \(-33843179482786377/26543104\) | \(-669393406186212606976\) | \([]\) | \(39536640\) | \(3.3029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 272734s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 272734s do not have complex multiplication.Modular form 272734.2.a.s
sage: E.q_eigenform(10)