Properties

Label 35904.l
Number of curves $4$
Conductor $35904$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 35904.l have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(11\)\(1 + T\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 2 T + 5 T^{2}\) 1.5.c
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 35904.l do not have complex multiplication.

Modular form 35904.2.a.l

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + 4 q^{7} + q^{9} - q^{11} - 2 q^{13} + 2 q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 35904.l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35904.l1 35904bv4 \([0, -1, 0, -162049, -1299551]\) \(3590504967602306/2071799959977\) \(271554964354105344\) \([4]\) \(393216\) \(2.0348\)  
35904.l2 35904bv2 \([0, -1, 0, -114529, -14842751]\) \(2535093488117092/7367303889\) \(482823627669504\) \([2, 2]\) \(196608\) \(1.6882\)  
35904.l3 35904bv1 \([0, -1, 0, -114449, -14864655]\) \(10119139303540048/85833\) \(1406287872\) \([2]\) \(98304\) \(1.3416\) \(\Gamma_0(N)\)-optimal
35904.l4 35904bv3 \([0, -1, 0, -68289, -26985375]\) \(-268702931670626/2248659199809\) \(-294736258637365248\) \([2]\) \(393216\) \(2.0348\)