Properties

Label 112710v
Number of curves $2$
Conductor $112710$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 112710v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112710.bd2 112710v1 \([1, 0, 1, -15179, -758794]\) \(-16022066761/998400\) \(-24098948889600\) \([2]\) \(394240\) \(1.3219\) \(\Gamma_0(N)\)-optimal
112710.bd1 112710v2 \([1, 0, 1, -246379, -47091274]\) \(68523370149961/243360\) \(5874118791840\) \([2]\) \(788480\) \(1.6684\)  

Rank

sage: E.rank()
 

The elliptic curves in class 112710v have rank \(0\).

Complex multiplication

The elliptic curves in class 112710v do not have complex multiplication.

Modular form 112710.2.a.v

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.