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Properties

Label 10710c
Number of curves $2$
Conductor $10710$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 10710c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10710.h2 10710c1 \([1, -1, 0, -474, -8092]\) \(-599077107/1132880\) \(-22298477040\) \([2]\) \(10752\) \(0.67547\) \(\Gamma_0(N)\)-optimal
10710.h1 10710c2 \([1, -1, 0, -9654, -362440]\) \(5055680349747/4081700\) \(80340101100\) \([2]\) \(21504\) \(1.0220\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10710c have rank \(0\).

Complex multiplication

The elliptic curves in class 10710c do not have complex multiplication.

Modular form 10710.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + 2 q^{11} + 6 q^{13} + q^{14} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})\) 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.