Elliptic curve isogeny class with Cremona label 234432bv (LMFDB label 234432.bv)

• Label: 234432bv
• Number of curves: $4$
• Conductor: $234432$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 234432bv have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 234432bv do not have complex multiplication.

Modular form 234432.2.a.bv

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 234432bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
234432.bv4	234432bv1	\([0, 0, 0, -885900, -117727504]\)	\(402355893390625/201513996288\)	\(38509924396289753088\)	\([2]\)	\(5308416\)	\(2.4509\)	\(\Gamma_0(N)\)-optimal
234432.bv3	234432bv2	\([0, 0, 0, -7705740, 8150646512]\)	\(264788619837198625/3058196150592\)	\(584430385569875361792\)	\([2]\)	\(10616832\)	\(2.7975\)
234432.bv2	234432bv3	\([0, 0, 0, -38901900, 93387642608]\)	\(34069730739753390625/1354703543952\)	\(258887878846974001152\)	\([2]\)	\(15925248\)	\(3.0002\)
234432.bv1	234432bv4	\([0, 0, 0, -622424460, 5976928910576]\)	\(139545621883503188502625/220644468\)	\(42165814472736768\)	\([2]\)	\(31850496\)	\(3.3468\)