Properties

Label 9240q
Number of curves $4$
Conductor $9240$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9240q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9240.a4 9240q1 \([0, -1, 0, 364, 2436]\) \(20777545136/23059575\) \(-5903251200\) \([4]\) \(4096\) \(0.56140\) \(\Gamma_0(N)\)-optimal
9240.a3 9240q2 \([0, -1, 0, -2056, 24700]\) \(939083699236/300155625\) \(307359360000\) \([2, 2]\) \(8192\) \(0.90798\)  
9240.a2 9240q3 \([0, -1, 0, -13056, -551700]\) \(120186986927618/4332064275\) \(8872067635200\) \([2]\) \(16384\) \(1.2545\)  
9240.a1 9240q4 \([0, -1, 0, -29776, 1987276]\) \(1425631925916578/270703125\) \(554400000000\) \([2]\) \(16384\) \(1.2545\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9240q have rank \(1\).

Complex multiplication

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

Modular form 9240.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} - 2 q^{13} + q^{15} - 2 q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.