Properties

Label 177744.j
Number of curves $1$
Conductor $177744$
CM no
Rank $0$

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

Elliptic curves in class 177744.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177744.j1 177744bk1 \([0, -1, 0, -4187195992, -104212207336976]\) \(25311095642246736793/20804234379264\) \(6673203577884742760911601664\) \([]\) \(195858432\) \(4.2677\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177744.j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 177744.j do not have complex multiplication.

Modular form 177744.2.a.j

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