Elliptic curve isogeny class with Cremona label 139650dv (LMFDB label 139650.ev)

• Label: 139650dv
• Number of curves: $4$
• Conductor: $139650$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 139650dv have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	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 139650dv do not have complex multiplication.

Modular form 139650.2.a.dv

Isogeny 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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 139650dv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139650.ev4	139650dv1	\([1, 1, 1, -57241213, 196325696531]\)	\(-11283450590382195961/2530373271552000\)	\(-4651498203512832000000000\)	\([2]\)	\(30965760\)	\(3.4535\)	\(\Gamma_0(N)\)-optimal
139650.ev3	139650dv2	\([1, 1, 1, -960409213, 11455217984531]\)	\(53294746224000958661881/1997017344000000\)	\(3671048336004000000000000\)	\([2, 2]\)	\(61931520\)	\(3.8000\)
139650.ev1	139650dv3	\([1, 1, 1, -15366409213, 733167005984531]\)	\(218289391029690300712901881/306514992000\)	\(563455973340750000000\)	\([2]\)	\(123863040\)	\(4.1466\)
139650.ev2	139650dv4	\([1, 1, 1, -1005097213, 10330599776531]\)	\(61085713691774408830201/10268551781250000000\)	\(18876325758004394531250000000\)	\([2]\)	\(123863040\)	\(4.1466\)