Elliptic curve isogeny class with Cremona label 162576e (LMFDB label 162576.g)

• Label: 162576e
• Number of curves: $2$
• Conductor: $162576$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 162576e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(1129\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162576e do not have complex multiplication.

Modular form 162576.2.a.e

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 162576e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162576.g2	162576e1	\([0, 0, 0, -423291, -103144790]\)	\(2809010351919673/86399552016\)	\(257987679926943744\)	\([2]\)	\(1376256\)	\(2.1167\)	\(\Gamma_0(N)\)-optimal
162576.g1	162576e2	\([0, 0, 0, -6721851, -6707814806]\)	\(11248714136064965113/11150559468\)	\(33295392162496512\)	\([2]\)	\(2752512\)	\(2.4632\)