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Properties

Label 10560.bq
Number of curves $6$
Conductor $10560$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 10560.bq have rank \(1\).

L-function data

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

Complex multiplication

The elliptic curves in class 10560.bq do not have complex multiplication.

Modular form 10560.2.a.bq

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 10560.bq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10560.bq1 10560t4 \([0, 1, 0, -211201, 37288415]\) \(15897679904620804/2475\) \(162201600\) \([2]\) \(32768\) \(1.4220\)  
10560.bq2 10560t5 \([0, 1, 0, -112001, -14188065]\) \(1185450336504002/26043266205\) \(3413542988021760\) \([2]\) \(65536\) \(1.7685\)  
10560.bq3 10560t3 \([0, 1, 0, -15201, 390015]\) \(5927735656804/2401490025\) \(157384050278400\) \([2, 2]\) \(32768\) \(1.4220\)  
10560.bq4 10560t2 \([0, 1, 0, -13201, 579215]\) \(15529488955216/6125625\) \(100362240000\) \([2, 2]\) \(16384\) \(1.0754\)  
10560.bq5 10560t1 \([0, 1, 0, -701, 11715]\) \(-37256083456/38671875\) \(-39600000000\) \([2]\) \(8192\) \(0.72881\) \(\Gamma_0(N)\)-optimal
10560.bq6 10560t6 \([0, 1, 0, 49599, 2891295]\) \(102949393183198/86815346805\) \(-11379061136424960\) \([2]\) \(65536\) \(1.7685\)