Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 77658.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.j1 77658h1 \([1, 1, 0, 843106, -25321833228]\) \(5670505847/23702740992\) \(-277042383842599002120192\) \([]\) \(11269440\) \(3.1771\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658.j1 has rank \(0\).

Complex multiplication

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

Modular form 77658.2.a.j

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