Properties

Label 107712.ey
Number of curves $2$
Conductor $107712$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ey1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 107712.ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
107712.ey1 107712cr1 [0, 0, 0, -112908, 14593520] [2] 589824 \(\Gamma_0(N)\)-optimal
107712.ey2 107712cr2 [0, 0, 0, -89868, 20722160] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 107712.ey have rank \(0\).

Complex multiplication

The elliptic curves in class 107712.ey do not have complex multiplication.

Modular form 107712.2.a.ey

sage: E.q_eigenform(10)
 
\( q + 4q^{5} - 2q^{7} + q^{11} + q^{17} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.