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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 209484bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.r1 | 209484bp1 | \([0, 0, 0, -3108933, -2109915971]\) | \(-51964534050048/253\) | \(-16179730524144\) | \([]\) | \(1622016\) | \(2.1563\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 209484bp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 209484bp do not have complex multiplication.Modular form 209484.2.a.bp
sage: E.q_eigenform(10)