Properties

Label 177870j
Number of curves $4$
Conductor $177870$
CM no
Rank $0$
Graph

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

Elliptic curves in class 177870j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177870.ie3 177870j1 [1, 0, 0, -20875, -734623] [2] 983040 \(\Gamma_0(N)\)-optimal
177870.ie2 177870j2 [1, 0, 0, -139455, 19495125] [2, 2] 1966080  
177870.ie1 177870j3 [1, 0, 0, -2214605, 1268320395] [2] 3932160  
177870.ie4 177870j4 [1, 0, 0, 38415, 65848047] [2] 3932160  

Rank

sage: E.rank()
 

The elliptic curves in class 177870j have rank \(0\).

Complex multiplication

The elliptic curves in class 177870j do not have complex multiplication.

Modular form 177870.2.a.j

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} + q^{12} - 2q^{13} + q^{15} + q^{16} - 6q^{17} + q^{18} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.