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Properties

Label 35490.l
Number of curves $6$
Conductor $35490$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 35490.l 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
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 35490.2.a.l

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 35490.l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35490.l1 35490i6 \([1, 1, 0, -10336888, -12796140482]\) \(25306558948218234961/4478906250\) \(21618824997656250\) \([2]\) \(1376256\) \(2.5309\)  
35490.l2 35490i4 \([1, 1, 0, -648118, -198801728]\) \(6237734630203441/82168222500\) \(396610315877002500\) \([2, 2]\) \(688128\) \(2.1843\)  
35490.l3 35490i5 \([1, 1, 0, -98868, -524287278]\) \(-22143063655441/24584858584650\) \(-118666416680115881850\) \([2]\) \(1376256\) \(2.5309\)  
35490.l4 35490i2 \([1, 1, 0, -76898, 3295908]\) \(10418796526321/5038160400\) \(24318237962163600\) \([2, 2]\) \(344064\) \(1.8378\)  
35490.l5 35490i1 \([1, 1, 0, -63378, 6110772]\) \(5832972054001/4542720\) \(21926841780480\) \([2]\) \(172032\) \(1.4912\) \(\Gamma_0(N)\)-optimal
35490.l6 35490i3 \([1, 1, 0, 278002, 25512648]\) \(492271755328079/342606902820\) \(-1653698081993701380\) \([2]\) \(688128\) \(2.1843\)