↑

Properties

Label 43560br
Number of curves $6$
Conductor $43560$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("br1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 43560br have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 2 T + 7 T^{2}\) 1.7.c
\(13\) \( 1 + 13 T^{2}\) 1.13.a
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 43560br do not have complex multiplication.

Modular form 43560.2.a.br

Copy content sage:E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 43560br

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43560.q5 43560br1 \([0, 0, 0, -190938, 53675237]\) \(-37256083456/38671875\) \(-799095805818750000\) \([2]\) \(491520\) \(2.1305\) \(\Gamma_0(N)\)-optimal
43560.q4 43560br2 \([0, 0, 0, -3594063, 2621673362]\) \(15529488955216/6125625\) \(2025228410267040000\) \([2, 2]\) \(983040\) \(2.4771\)  
43560.q3 43560br3 \([0, 0, 0, -4138563, 1774758062]\) \(5927735656804/2401490025\) \(3175882183844361446400\) \([2, 2]\) \(1966080\) \(2.8236\)  
43560.q1 43560br4 \([0, 0, 0, -57499563, 167820468662]\) \(15897679904620804/2475\) \(3273096420633600\) \([2]\) \(1966080\) \(2.8236\)  
43560.q6 43560br5 \([0, 0, 0, 13503237, 12913790582]\) \(102949393183198/86815346805\) \(-229620202734149609564160\) \([2]\) \(3932160\) \(3.1702\)  
43560.q2 43560br6 \([0, 0, 0, -30492363, -63566853658]\) \(1185450336504002/26043266205\) \(68882522341166464296960\) \([2]\) \(3932160\) \(3.1702\)