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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 104742.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104742.w1 | 104742h1 | \([1, -1, 0, 20394, -1279476]\) | \(105756712489/140300424\) | \(-1244428703671032\) | \([]\) | \(539136\) | \(1.5823\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 104742.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 104742.w do not have complex multiplication.Modular form 104742.2.a.w
sage: E.q_eigenform(10)