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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 805.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
805.c1 | 805a1 | \([0, -1, 1, 23004, 2393001]\) | \(1346216501445963776/3268768272021875\) | \(-3268768272021875\) | \([]\) | \(5720\) | \(1.6608\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 805.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 805.c do not have complex multiplication.Modular form 805.2.a.c
sage: E.q_eigenform(10)