Elliptic curve isogeny class with LMFDB label 43706.x (Cremona label 43706v)

• Label: 43706.x
• Number of curves: $2$
• Conductor: $43706$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 43706.x have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(13\)	\(1 - T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 43706.x do not have complex multiplication.

Modular form 43706.2.a.x

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 43706.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
43706.x1	43706v2	\([1, -1, 1, -357528, -90190667]\)	\(-1064019559329/125497034\)	\(-596123993436321194\)	\([]\)	\(987840\)	\(2.1466\)
43706.x2	43706v1	\([1, -1, 1, -4518, 179893]\)	\(-2146689/1664\)	\(-7904173457024\)	\([]\)	\(141120\)	\(1.1736\)	\(\Gamma_0(N)\)-optimal