Elliptic curve isogeny class with Cremona label 17600cd (LMFDB label 17600.cd)

• Label: 17600cd
• Number of curves: $3$
• Conductor: $17600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 17600cd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17600cd do not have complex multiplication.

Modular form 17600.2.a.cd

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 17600cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17600.cd3	17600cd1	\([0, 1, 0, -33, -187]\)	\(-4096/11\)	\(-11000000\)	\([]\)	\(2240\)	\(0.038564\)	\(\Gamma_0(N)\)-optimal
17600.cd2	17600cd2	\([0, 1, 0, -1033, 22813]\)	\(-122023936/161051\)	\(-161051000000\)	\([]\)	\(11200\)	\(0.84328\)
17600.cd1	17600cd3	\([0, 1, 0, -782033, 265925813]\)	\(-52893159101157376/11\)	\(-11000000\)	\([]\)	\(56000\)	\(1.6480\)