Elliptic curve isogeny class with Cremona label 23716e (LMFDB label 23716.i)

• Label: 23716e
• Number of curves: $2$
• Conductor: $23716$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 23716e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 23716e do not have complex multiplication.

Modular form 23716.2.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 23716e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23716.i2	23716e1	\([0, -1, 0, -173917, -26539302]\)	\(131072/7\)	\(31069941044627408\)	\([2]\)	\(228096\)	\(1.9211\)	\(\Gamma_0(N)\)-optimal
23716.i1	23716e2	\([0, -1, 0, -500012, 102463880]\)	\(194672/49\)	\(3479833396998269696\)	\([2]\)	\(456192\)	\(2.2677\)