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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1339.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1339.a1 | 1339a1 | \([1, 1, 0, -137, -602]\) | \(287626699801/38243179\) | \(38243179\) | \([]\) | \(280\) | \(0.18272\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1339.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1339.a do not have complex multiplication.Modular form 1339.2.a.a
sage: E.q_eigenform(10)