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Properties

Label 32490bn
Number of curves $4$
Conductor $32490$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bn1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 32490bn have rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 32490bn do not have complex multiplication.

Modular form 32490.2.a.bn

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 32490bn

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.bf4 32490bn1 \([1, -1, 1, 30329347, -136709816763]\) \(89962967236397039/287450726400000\) \(-9858538674664331673600000\) \([2]\) \(6912000\) \(3.4791\) \(\Gamma_0(N)\)-optimal
32490.bf3 32490bn2 \([1, -1, 1, -285733373, -1601597311419]\) \(75224183150104868881/11219310000000000\) \(384782473585178190000000000\) \([2]\) \(13824000\) \(3.8256\)  
32490.bf2 32490bn3 \([1, -1, 1, -10726459853, -427592566016283]\) \(-3979640234041473454886161/1471455901872240\) \(-50465709717790999497467760\) \([2]\) \(34560000\) \(4.2838\)  
32490.bf1 32490bn4 \([1, -1, 1, -171623372873, -27366047842833219]\) \(16300610738133468173382620881/2228489100\) \(76429258863121485900\) \([2]\) \(69120000\) \(4.6304\)