Properties

Label 77658.s
Number of curves $1$
Conductor $77658$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 77658.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.s1 77658o1 \([1, 0, 1, -667528, 209397374]\) \(65450827/168\) \(84435558805389624\) \([]\) \(1543872\) \(2.1241\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658.s1 has rank \(0\).

Complex multiplication

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

Modular form 77658.2.a.s

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