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

• Label: 17600dd
• Number of curves: $3$
• Conductor: $17600$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 17600dd have rank \(2\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 17600.2.a.dd

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 17600dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17600.bc2	17600dd1	\([0, -1, 0, -1793, 29857]\)	\(-19465109/22\)	\(-720896000\)	\([]\)	\(9216\)	\(0.61341\)	\(\Gamma_0(N)\)-optimal
17600.bc3	17600dd2	\([0, -1, 0, 12607, -310943]\)	\(6761990971/5153632\)	\(-168874213376000\)	\([]\)	\(46080\)	\(1.4181\)
17600.bc1	17600dd3	\([0, -1, 0, -1940993, -1040206943]\)	\(-24680042791780949/369098752\)	\(-12094627905536000\)	\([]\)	\(230400\)	\(2.2228\)