Elliptic curve isogeny class with Cremona label 366912ex (LMFDB label 366912.ex)

• Label: 366912ex
• Number of curves: $2$
• Conductor: $366912$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 366912ex have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 366912ex do not have complex multiplication.

Modular form 366912.2.a.ex

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 366912ex

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
366912.ex1	366912ex1	\([0, 0, 0, -1052671116, 13145793507056]\)	\(16728308209329751/16376256\)	\(126288681524967707246592\)	\([2]\)	\(92897280\)	\(3.7264\)	\(\Gamma_0(N)\)-optimal
366912.ex2	366912ex2	\([0, 0, 0, -1044768396, 13352885865200]\)	\(-16354376146655191/523792501128\)	\(-4039327692490901495318839296\)	\([2]\)	\(185794560\)	\(4.0729\)