Elliptic curve isogeny class with Cremona label 15600j (LMFDB label 15600.c)

• Label: 15600j
• Number of curves: $2$
• Conductor: $15600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 15600j have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 15600j do not have complex multiplication.

Modular form 15600.2.a.j

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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 15600j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15600.c1	15600j1	\([0, -1, 0, -83, 162]\)	\(256000/117\)	\(29250000\)	\([2]\)	\(4608\)	\(0.12754\)	\(\Gamma_0(N)\)-optimal
15600.c2	15600j2	\([0, -1, 0, 292, 912]\)	\(686000/507\)	\(-2028000000\)	\([2]\)	\(9216\)	\(0.47412\)