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Properties

Label 35490k
Number of curves $8$
Conductor $35490$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("k1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 35490k 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 \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 + 7 T + 17 T^{2}\) 1.17.h
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 - 9 T + 23 T^{2}\) 1.23.aj
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 35490.2.a.k

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 35490k

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35490.f7 35490k1 \([1, 1, 0, -3677443, 2748786253]\) \(-1139466686381936641/17587891077120\) \(-84893390942062510080\) \([2]\) \(1376256\) \(2.6262\) \(\Gamma_0(N)\)-optimal
35490.f5 35490k2 \([1, 1, 0, -59055363, 174652925517]\) \(4718909406724749250561/1098974822400\) \(5304541563533721600\) \([2, 2]\) \(2752512\) \(2.9728\)  
35490.f4 35490k3 \([1, 1, 0, -59271683, 173308669773]\) \(4770955732122964500481/71987251059360000\) \(347468711298578382240000\) \([2, 2]\) \(5505024\) \(3.3193\)  
35490.f2 35490k4 \([1, 1, 0, -944885763, 11178969652557]\) \(19328649688935739391016961/1048320\) \(5060040410880\) \([2]\) \(5505024\) \(3.3193\)  
35490.f6 35490k5 \([1, 1, 0, -5610803, 475516013757]\) \(-4047051964543660801/20235220197806250000\) \(-97671542967752987756250000\) \([2]\) \(11010048\) \(3.6659\)  
35490.f3 35490k6 \([1, 1, 0, -116393683, -214926715427]\) \(36128658497509929012481/16775330746084419600\) \(80971317423176991285056400\) \([2, 2]\) \(11010048\) \(3.6659\)  
35490.f8 35490k7 \([1, 1, 0, 411106017, -1621979415207]\) \(1591934139020114746758719/1156766383092650262660\) \(-5583490388809052121659651940\) \([2]\) \(22020096\) \(4.0125\)  
35490.f1 35490k8 \([1, 1, 0, -1557845383, -23653796228447]\) \(86623684689189325642735681/56690726941459561860\) \(273635311017579486321904740\) \([2]\) \(22020096\) \(4.0125\)