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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 104742r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104742.b1 | 104742r1 | \([1, -1, 0, -2818611, -1818626477]\) | \(22947463187713/29878794\) | \(3224464563555604314\) | \([]\) | \(3379200\) | \(2.4585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 104742r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 104742r do not have complex multiplication.Modular form 104742.2.a.r
sage: E.q_eigenform(10)