Elliptic curve isogeny class with Cremona label 8464m (LMFDB label 8464.g)

• Label: 8464m
• Number of curves: $2$
• Conductor: $8464$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 8464m have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8464m do not have complex multiplication.

Modular form 8464.2.a.m

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 8464m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8464.g2	8464m1	\([0, 0, 0, -86227, -11315310]\)	\(-116930169/23552\)	\(-14280872991653888\)	\([2]\)	\(63360\)	\(1.8224\)	\(\Gamma_0(N)\)-optimal
8464.g1	8464m2	\([0, 0, 0, -1440467, -665413230]\)	\(545138290809/16928\)	\(10264377462751232\)	\([2]\)	\(126720\)	\(2.1690\)