Elliptic curve isogeny class with LMFDB label 13650.cx (Cremona label 13650cp)

• Label: 13650.cx
• Number of curves: $4$
• Conductor: $13650$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 13650.cx have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 13650.cx do not have complex multiplication.

Modular form 13650.2.a.cx

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 13650.cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13650.cx1	13650cp3	\([1, 0, 0, -2240088, -1290650208]\)	\(79560762543506753209/479824800\)	\(7497262500000\)	\([2]\)	\(245760\)	\(2.0785\)
13650.cx2	13650cp2	\([1, 0, 0, -140088, -20150208]\)	\(19458380202497209/47698560000\)	\(745290000000000\)	\([2, 2]\)	\(122880\)	\(1.7319\)
13650.cx3	13650cp4	\([1, 0, 0, -88088, -35282208]\)	\(-4837870546133689/31603162500000\)	\(-493799414062500000\)	\([2]\)	\(245760\)	\(2.0785\)
13650.cx4	13650cp1	\([1, 0, 0, -12088, -54208]\)	\(12501706118329/7156531200\)	\(111820800000000\)	\([2]\)	\(61440\)	\(1.3854\)	\(\Gamma_0(N)\)-optimal