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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 56784c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56784.b1 | 56784c1 | \([0, -1, 0, -4697, -175371]\) | \(-20380171264/12252303\) | \(-6891087280896\) | \([]\) | \(161280\) | \(1.1657\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56784c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 56784c do not have complex multiplication.Modular form 56784.2.a.c
sage: E.q_eigenform(10)