Properties

Label 10710bm
Number of curves $2$
Conductor $10710$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10710bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10710.bj2 10710bm1 \([1, -1, 1, 733, -9309]\) \(59822347031/83966400\) \(-61211505600\) \([2]\) \(9216\) \(0.75542\) \(\Gamma_0(N)\)-optimal
10710.bj1 10710bm2 \([1, -1, 1, -4667, -89229]\) \(15417797707369/4080067320\) \(2974369076280\) \([2]\) \(18432\) \(1.1020\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10710bm have rank \(1\).

Complex multiplication

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

Modular form 10710.2.a.bm

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