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Properties

Label 15162l
Number of curves $6$
Conductor $15162$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 15162l have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(7\)\(1 + T\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(13\) \( 1 - 5 T + 13 T^{2}\) 1.13.af
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(23\) \( 1 - 5 T + 23 T^{2}\) 1.23.af
\(29\) \( 1 - 8 T + 29 T^{2}\) 1.29.ai
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 15162l do not have complex multiplication.

Modular form 15162.2.a.l

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2 q^{10} - 4 q^{11} + q^{12} - 6 q^{13} + q^{14} - 2 q^{15} + q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 15162l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15162.j5 15162l1 \([1, 0, 1, -1452, -47126]\) \(-7189057/16128\) \(-758755968768\) \([2]\) \(27648\) \(0.96817\) \(\Gamma_0(N)\)-optimal
15162.j4 15162l2 \([1, 0, 1, -30332, -2034070]\) \(65597103937/63504\) \(2987601627024\) \([2, 2]\) \(55296\) \(1.3147\)  
15162.j1 15162l3 \([1, 0, 1, -485192, -130122646]\) \(268498407453697/252\) \(11855562012\) \([2]\) \(110592\) \(1.6613\)  
15162.j3 15162l4 \([1, 0, 1, -37552, -994390]\) \(124475734657/63011844\) \(2964447714414564\) \([2, 2]\) \(110592\) \(1.6613\)  
15162.j2 15162l5 \([1, 0, 1, -329962, 72225074]\) \(84448510979617/933897762\) \(43936042977218322\) \([2]\) \(221184\) \(2.0079\)  
15162.j6 15162l6 \([1, 0, 1, 139338, -7645454]\) \(6359387729183/4218578658\) \(-198466749533407698\) \([2]\) \(221184\) \(2.0079\)