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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 21175x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21175.x1 | 21175x1 | \([1, -1, 0, 2183, 6166]\) | \(1382658525/823543\) | \(-685084833125\) | \([]\) | \(48384\) | \(0.96039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21175x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 21175x do not have complex multiplication.Modular form 21175.2.a.x
sage: E.q_eigenform(10)