↑

Properties

Label 146523s
Number of curves $6$
Conductor $146523$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("s1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 146523s have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1 + T\)
\(13\)\(1\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 - T + 2 T^{2}\) 1.2.ab
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(7\) \( 1 + 3 T + 7 T^{2}\) 1.7.d
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(23\) \( 1 + 3 T + 23 T^{2}\) 1.23.d
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 146523s do not have complex multiplication.

Modular form 146523.2.a.s

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - 3 q^{8} + q^{9} - 2 q^{10} + 4 q^{11} - q^{12} - 2 q^{15} - q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 146523s

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.y4 146523s1 \([1, 0, 1, -26326317, 51989348491]\) \(17319700013617/25857\) \(3012532754224259097\) \([2]\) \(6193152\) \(2.8145\) \(\Gamma_0(N)\)-optimal
146523.y3 146523s2 \([1, 0, 1, -26570522, 50975604695]\) \(17806161424897/668584449\) \(77895059425976667471129\) \([2, 2]\) \(12386304\) \(3.1611\)  
146523.y5 146523s3 \([1, 0, 1, 10792843, 182957955221]\) \(1193377118543/124806800313\) \(-14540920210884441827731473\) \([2]\) \(24772608\) \(3.5077\)  
146523.y2 146523s4 \([1, 0, 1, -67841167, -145885371955]\) \(296380748763217/92608836489\) \(10789618024276259223855969\) \([2, 2]\) \(24772608\) \(3.5077\)  
146523.y6 146523s5 \([1, 0, 1, 189306698, -987890341111]\) \(6439735268725823/7345472585373\) \(-855802171895135276956955733\) \([2]\) \(49545216\) \(3.8542\)  
146523.y1 146523s6 \([1, 0, 1, -985319352, -11902817825819]\) \(908031902324522977/161726530797\) \(18842343321074404250124837\) \([2]\) \(49545216\) \(3.8542\)