Show commands:
SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 75712.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.bp1 | 75712bq1 | \([0, 0, 0, -9308, -346736]\) | \(-32209663824/117649\) | \(-325757845504\) | \([]\) | \(82944\) | \(1.0700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.bp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75712.bp do not have complex multiplication.Modular form 75712.2.a.bp
sage: E.q_eigenform(10)