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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 39039.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39039.p1 | 39039t1 | \([0, 1, 1, -5540045, 5018901008]\) | \(-3895861901277528064/1561102682139\) | \(-7535144476072664451\) | \([]\) | \(940800\) | \(2.5858\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39039.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 39039.p do not have complex multiplication.Modular form 39039.2.a.p
sage: E.q_eigenform(10)