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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 111573.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111573.x1 | 111573r1 | \([1, -1, 0, -632256, 83357441]\) | \(950152003191/448204933\) | \(13185193891150888299\) | \([]\) | \(2283008\) | \(2.3630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 111573.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 111573.x do not have complex multiplication.Modular form 111573.2.a.x
sage: E.q_eigenform(10)