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Properties

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

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 10710bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10710.bh2 10710bj1 \([1, -1, 1, -15152, 1880979]\) \(-527690404915129/1782829440000\) \(-1299682661760000\) \([2]\) \(61440\) \(1.5862\) \(\Gamma_0(N)\)-optimal
10710.bh1 10710bj2 \([1, -1, 1, -339152, 76012179]\) \(5918043195362419129/8515734343200\) \(6207970336192800\) \([2]\) \(122880\) \(1.9328\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10710.2.a.bj

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