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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 193200.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.br1 | 193200dn1 | \([0, -1, 0, -2052608, 1138163712]\) | \(-14943832855786297/85501108224\) | \(-5472070926336000000\) | \([]\) | \(4043520\) | \(2.4373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193200.br1 has rank \(1\).
Complex multiplication
The elliptic curves in class 193200.br do not have complex multiplication.Modular form 193200.2.a.br
sage: E.q_eigenform(10)