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Properties

Label 194040.ev
Number of curves $6$
Conductor $194040$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ev1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 194040.ev have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(11\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 - 4 T + 19 T^{2}\) 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 194040.ev do not have complex multiplication.

Modular form 194040.2.a.ev

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} + q^{11} + 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 194040.ev

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
194040.ev1 194040ci3 \([0, 0, 0, -23284947, 43247498686]\) \(15897679904620804/2475\) \(217365657062400\) \([2]\) \(6291456\) \(2.5976\)  
194040.ev2 194040ci6 \([0, 0, 0, -12348147, -16381240274]\) \(1185450336504002/26043266205\) \(4574474077333997168640\) \([2]\) \(12582912\) \(2.9442\)  
194040.ev3 194040ci4 \([0, 0, 0, -1675947, 457356886]\) \(5927735656804/2401490025\) \(210909679681989657600\) \([2, 2]\) \(6291456\) \(2.5976\)  
194040.ev4 194040ci2 \([0, 0, 0, -1455447, 675607786]\) \(15529488955216/6125625\) \(134495000307360000\) \([2, 2]\) \(3145728\) \(2.2511\)  
194040.ev5 194040ci1 \([0, 0, 0, -77322, 13832161]\) \(-37256083456/38671875\) \(-53067787368750000\) \([2]\) \(1572864\) \(1.9045\) \(\Gamma_0(N)\)-optimal
194040.ev6 194040ci5 \([0, 0, 0, 5468253, 3327896446]\) \(102949393183198/86815346805\) \(-15249030223328447293440\) \([2]\) \(12582912\) \(2.9442\)