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Properties

Label 35490cv
Number of curves $4$
Conductor $35490$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 35490cv have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 - T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 + 2 T + 23 T^{2}\) 1.23.c
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 35490cv do not have complex multiplication.

Modular form 35490.2.a.cv

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + q^{14} - q^{15} + q^{16} - 6 q^{17} + q^{18} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 35490cv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35490.cs4 35490cv1 \([1, 1, 1, -121687355, 261689364425]\) \(41285728533151645510969/17760741842188800000\) \(85727708570553479539200000\) \([2]\) \(19353600\) \(3.6725\) \(\Gamma_0(N)\)-optimal
35490.cs2 35490cv2 \([1, 1, 1, -1666266235, 26167984171337]\) \(105997782562506306791694649/51649016225625000000\) \(249299936358992780625000000\) \([2, 2]\) \(38707200\) \(4.0190\)  
35490.cs3 35490cv3 \([1, 1, 1, -1388653315, 35173858341305]\) \(-61354313914516350666047929/75227254486083984375000\) \(-363107588998720550537109375000\) \([2]\) \(77414400\) \(4.3656\)  
35490.cs1 35490cv4 \([1, 1, 1, -26657141235, 1675195869221337]\) \(434014578033107719741685694649/103121648659575000\) \(497748501844874546175000\) \([2]\) \(77414400\) \(4.3656\)