Properties

Label 77658bo
Number of curves $1$
Conductor $77658$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 77658bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.bf1 77658bo1 \([1, 0, 0, -5779, 171425]\) \(-11543820929593/224042112\) \(-414253865088\) \([]\) \(112896\) \(1.0228\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658bo1 has rank \(1\).

Complex multiplication

The elliptic curves in class 77658bo do not have complex multiplication.

Modular form 77658.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 2 q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 2 q^{10} - q^{11} + q^{12} + 2 q^{13} + q^{14} - 2 q^{15} + q^{16} + 3 q^{17} + q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display