Elliptic curve isogeny class with Cremona label 82368bv (LMFDB label 82368.bb)

• Label: 82368bv
• Number of curves: $4$
• Conductor: $82368$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 82368bv have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 82368bv do not have complex multiplication.

Modular form 82368.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 82368bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82368.bb4	82368bv1	\([0, 0, 0, -88716, -11824400]\)	\(-404075127457/82223856\)	\(-15713223579795456\)	\([2]\)	\(442368\)	\(1.8301\)	\(\Gamma_0(N)\)-optimal
82368.bb3	82368bv2	\([0, 0, 0, -1482636, -694845200]\)	\(1886079023633377/59629284\)	\(11395333629149184\)	\([2, 2]\)	\(884736\)	\(2.1767\)
82368.bb2	82368bv3	\([0, 0, 0, -1545996, -632220176]\)	\(2138362647385537/333926700822\)	\(63814386292945846272\)	\([2]\)	\(1769472\)	\(2.5233\)
82368.bb1	82368bv4	\([0, 0, 0, -23721996, -44470801424]\)	\(7725203825376001537/7722\)	\(1475697180672\)	\([2]\)	\(1769472\)	\(2.5233\)