Elliptic curve isogeny class with Cremona label 31680bv (LMFDB label 31680.dv)

• Label: 31680bv
• Number of curves: $2$
• Conductor: $31680$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 31680bv have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 6 T + 23 T^{2}\)	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 31680bv do not have complex multiplication.

Modular form 31680.2.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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 31680bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31680.dv2	31680bv1	\([0, 0, 0, 5748, 677104]\)	\(109902239/1100000\)	\(-210213273600000\)	\([]\)	\(115200\)	\(1.4294\)	\(\Gamma_0(N)\)-optimal
31680.dv1	31680bv2	\([0, 0, 0, -3421452, 2435924464]\)	\(-23178622194826561/1610510\)	\(-307773253877760\)	\([]\)	\(576000\)	\(2.2341\)