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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 4704.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.w1 | 4704bb1 | \([0, 1, 0, 152864, 2188556]\) | \(2731405432/1594323\) | \(-230582674642650624\) | \([]\) | \(43680\) | \(2.0210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4704.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4704.w do not have complex multiplication.Modular form 4704.2.a.w
sage: E.q_eigenform(10)