Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 77658b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.i1 77658b1 \([1, 1, 0, -10685409, -13672229067]\) \(-11543820929593/224042112\) \(-2618649075672714333312\) \([]\) \(4854528\) \(2.9034\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658b1 has rank \(1\).

Complex multiplication

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

Modular form 77658.2.a.b

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