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Properties

Label 19110.ce
Number of curves $4$
Conductor $19110$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ce1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 19110.ce have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 19110.ce do not have complex multiplication.

Modular form 19110.2.a.ce

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{12} + q^{13} - q^{15} + q^{16} - 2 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 19110.ce

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.ce1 19110cd3 \([1, 1, 1, -2063685, 76035357]\) \(8261629364934163009/4759323790524030\) \(559929684631361605470\) \([2]\) \(983040\) \(2.6708\)  
19110.ce2 19110cd2 \([1, 1, 1, -1468335, 682577937]\) \(2975849362756797409/8263842596100\) \(972232817588568900\) \([2, 2]\) \(491520\) \(2.3242\)  
19110.ce3 19110cd1 \([1, 1, 1, -1467355, 683537945]\) \(2969894891179808929/22997520\) \(2705635230480\) \([4]\) \(245760\) \(1.9776\) \(\Gamma_0(N)\)-optimal
19110.ce4 19110cd4 \([1, 1, 1, -888665, 1227699605]\) \(-659704930833045889/5156082432978750\) \(-606607942157516958750\) \([2]\) \(983040\) \(2.6708\)