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Properties

Label 9240.m
Number of curves $6$
Conductor $9240$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("m1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 + T\)
\(11\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 9240.2.a.m

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

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 9240.m

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9240.m1 9240u5 \([0, -1, 0, -1034880, -404867988]\) \(59850000883110493442/24255\) \(49674240\) \([2]\) \(65536\) \(1.7274\)  
9240.m2 9240u3 \([0, -1, 0, -64680, -6309828]\) \(29224056825643684/588305025\) \(602424345600\) \([2, 2]\) \(32768\) \(1.3808\)  
9240.m3 9240u6 \([0, -1, 0, -62480, -6761268]\) \(-13171152353214242/2080257264855\) \(-4260366878423040\) \([2]\) \(65536\) \(1.7274\)  
9240.m4 9240u2 \([0, -1, 0, -4180, -90428]\) \(31558509702736/4035425625\) \(1033068960000\) \([2, 4]\) \(16384\) \(1.0342\)  
9240.m5 9240u1 \([0, -1, 0, -1055, 12072]\) \(8124052043776/992578125\) \(15881250000\) \([4]\) \(8192\) \(0.68764\) \(\Gamma_0(N)\)-optimal
9240.m6 9240u4 \([0, -1, 0, 6320, -481028]\) \(27258770992316/112538412525\) \(-115239334425600\) \([4]\) \(32768\) \(1.3808\)