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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 212415bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212415.cn1 | 212415bt1 | \([1, 0, 1, -8138079178, 282572611137401]\) | \(-72628961394279272329/24608375505\) | \(-20195869525163740174360545\) | \([]\) | \(163918080\) | \(4.2127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 212415bt1 has rank \(1\).
Complex multiplication
The elliptic curves in class 212415bt do not have complex multiplication.Modular form 212415.2.a.bt
sage: E.q_eigenform(10)