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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 21675.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21675.w1 | 21675n1 | \([0, -1, 1, -204708, -31348807]\) | \(69632/9\) | \(122620736267578125\) | \([]\) | \(342720\) | \(2.0076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21675.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21675.w do not have complex multiplication.Modular form 21675.2.a.w
sage: E.q_eigenform(10)