Properties

Label 9240.c
Number of curves $4$
Conductor $9240$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9240.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9240.c1 9240b3 \([0, -1, 0, -16294696, -22417652180]\) \(233632133015204766393938/29145526885986328125\) \(59690039062500000000000\) \([2]\) \(983040\) \(3.0999\)  
9240.c2 9240b2 \([0, -1, 0, -4070176, 2799087676]\) \(7282213870869695463556/912102595400390625\) \(933993057690000000000\) \([2, 2]\) \(491520\) \(2.7534\)  
9240.c3 9240b1 \([0, -1, 0, -3938956, 3010246900]\) \(26401417552259125806544/507547744790625\) \(129932222666400000\) \([2]\) \(245760\) \(2.4068\) \(\Gamma_0(N)\)-optimal
9240.c4 9240b4 \([0, -1, 0, 6054824, 14499537676]\) \(11986661998777424518222/51295853620928503125\) \(-105053908215661574400000\) \([2]\) \(983040\) \(3.0999\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9240.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - q^{11} + 2 q^{13} + q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.