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

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

Rank

The elliptic curves in class 17600e 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 17600.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 17600e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17600.bj3	17600e1	\([0, -1, 0, -33, 187]\)	\(-4096/11\)	\(-11000000\)	\([]\)	\(2240\)	\(0.038564\)	\(\Gamma_0(N)\)-optimal
17600.bj2	17600e2	\([0, -1, 0, -1033, -22813]\)	\(-122023936/161051\)	\(-161051000000\)	\([]\)	\(11200\)	\(0.84328\)
17600.bj1	17600e3	\([0, -1, 0, -782033, -265925813]\)	\(-52893159101157376/11\)	\(-11000000\)	\([]\)	\(56000\)	\(1.6480\)