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Properties

Label 8190.g
Number of curves $6$
Conductor $8190$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("g1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 8190.g have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1 + T\)
\(13\)\(1 - T\)
 
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.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 8190.g do not have complex multiplication.

Modular form 8190.2.a.g

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 4 q^{11} + q^{13} + q^{14} + q^{16} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 8190.g

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8190.g1 8190k5 \([1, -1, 0, -550485, 157342675]\) \(25306558948218234961/4478906250\) \(3265122656250\) \([2]\) \(65536\) \(1.7977\)  
8190.g2 8190k3 \([1, -1, 0, -34515, 2448481]\) \(6237734630203441/82168222500\) \(59900634202500\) \([2, 2]\) \(32768\) \(1.4512\)  
8190.g3 8190k6 \([1, -1, 0, -5265, 6444031]\) \(-22143063655441/24584858584650\) \(-17922361908209850\) \([2]\) \(65536\) \(1.7977\)  
8190.g4 8190k2 \([1, -1, 0, -4095, -39875]\) \(10418796526321/5038160400\) \(3672818931600\) \([2, 2]\) \(16384\) \(1.1046\)  
8190.g5 8190k1 \([1, -1, 0, -3375, -74579]\) \(5832972054001/4542720\) \(3311642880\) \([2]\) \(8192\) \(0.75802\) \(\Gamma_0(N)\)-optimal
8190.g6 8190k4 \([1, -1, 0, 14805, -315815]\) \(492271755328079/342606902820\) \(-249760432155780\) \([2]\) \(32768\) \(1.4512\)