Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 77658.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.l1 77658n1 \([1, 1, 0, -179391, -26875323]\) \(100999381393/9362304\) \(59182522559104896\) \([]\) \(1034880\) \(1.9570\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658.l1 has rank \(1\).

Complex multiplication

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

Modular form 77658.2.a.l

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