↑

Properties

Label 960.l
Number of curves $8$
Conductor $960$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("l1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 960.l have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 960.l do not have complex multiplication.

Modular form 960.2.a.l

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 960.l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
960.l1 960g7 \([0, 1, 0, -138241, -19829665]\) \(1114544804970241/405\) \(106168320\) \([2]\) \(2048\) \(1.3306\)  
960.l2 960g5 \([0, 1, 0, -8641, -311905]\) \(272223782641/164025\) \(42998169600\) \([2, 2]\) \(1024\) \(0.98402\)  
960.l3 960g8 \([0, 1, 0, -7041, -429345]\) \(-147281603041/215233605\) \(-56422198149120\) \([2]\) \(2048\) \(1.3306\)  
960.l4 960g4 \([0, 1, 0, -5121, 139359]\) \(56667352321/15\) \(3932160\) \([2]\) \(512\) \(0.63744\)  
960.l5 960g3 \([0, 1, 0, -641, -3105]\) \(111284641/50625\) \(13271040000\) \([2, 2]\) \(512\) \(0.63744\)  
960.l6 960g2 \([0, 1, 0, -321, 2079]\) \(13997521/225\) \(58982400\) \([2, 2]\) \(256\) \(0.29087\)  
960.l7 960g1 \([0, 1, 0, -1, 95]\) \(-1/15\) \(-3932160\) \([2]\) \(128\) \(-0.055704\) \(\Gamma_0(N)\)-optimal
960.l8 960g6 \([0, 1, 0, 2239, -20961]\) \(4733169839/3515625\) \(-921600000000\) \([2]\) \(1024\) \(0.98402\)