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Properties

Label 61710bj
Number of curves $2$
Conductor $61710$
CM no
Rank $0$
Graph

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

Elliptic curves in class 61710bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.bj2 61710bj1 \([1, 0, 1, -106483, -5898994]\) \(75370704203521/35157196800\) \(62283118720204800\) \([2]\) \(645120\) \(1.9170\) \(\Gamma_0(N)\)-optimal
61710.bj1 61710bj2 \([1, 0, 1, -1422963, -653080562]\) \(179865548102096641/119964240000\) \(212523968978640000\) \([2]\) \(1290240\) \(2.2636\)  

Rank

sage: E.rank()
 

The elliptic curves in class 61710bj have rank \(0\).

Complex multiplication

The elliptic curves in class 61710bj do not have complex multiplication.

Modular form 61710.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2 q^{7} - q^{8} + q^{9} - q^{10} + q^{12} + 4 q^{13} - 2 q^{14} + q^{15} + q^{16} - q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.