Properties

Label 9240.j
Number of curves $2$
Conductor $9240$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 9240.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9240.j1 9240t1 \([0, -1, 0, -6280, 193660]\) \(26752959989284/169785\) \(173859840\) \([2]\) \(9984\) \(0.76623\) \(\Gamma_0(N)\)-optimal
9240.j2 9240t2 \([0, -1, 0, -6160, 201292]\) \(-12624273557282/1067664675\) \(-2186577254400\) \([2]\) \(19968\) \(1.1128\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9240.j have rank \(0\).

Complex multiplication

The elliptic curves in class 9240.j do not have complex multiplication.

Modular form 9240.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + q^{11} - 4 q^{13} - q^{15} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.