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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 50715bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50715.bw1 | 50715bt1 | \([0, 0, 1, -44247, 4071667]\) | \(-111701610496/18862875\) | \(-1617795619657875\) | \([]\) | \(359424\) | \(1.6450\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 50715bt1 has rank \(1\).
Complex multiplication
The elliptic curves in class 50715bt do not have complex multiplication.Modular form 50715.2.a.bt
sage: E.q_eigenform(10)