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SageMath
E = EllipticCurve("xt1")
E.isogeny_class()
Elliptic curves in class 235200xt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.xt1 | 235200xt1 | \([0, 1, 0, -19742753, 33781432383]\) | \(-1103770289367265/891813888\) | \(-687610344959587123200\) | \([]\) | \(21012480\) | \(2.9279\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 235200xt1 has rank \(1\).
Complex multiplication
The elliptic curves in class 235200xt do not have complex multiplication.Modular form 235200.2.a.xt
sage: E.q_eigenform(10)