Elliptic curve isogeny class with LMFDB label 15600.cu (Cremona label 15600cc)

• Label: 15600.cu
• Number of curves: $4$
• Conductor: $15600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 15600.cu have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 15600.2.a.cu

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 15600.cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15600.cu1	15600cc4	\([0, 1, 0, -478408, 120723188]\)	\(189208196468929/10860320250\)	\(695060496000000000\)	\([2]\)	\(165888\)	\(2.1777\)
15600.cu2	15600cc2	\([0, 1, 0, -82408, -9092812]\)	\(967068262369/4928040\)	\(315394560000000\)	\([2]\)	\(55296\)	\(1.6284\)
15600.cu3	15600cc1	\([0, 1, 0, -2408, -292812]\)	\(-24137569/561600\)	\(-35942400000000\)	\([2]\)	\(27648\)	\(1.2818\)	\(\Gamma_0(N)\)-optimal
15600.cu4	15600cc3	\([0, 1, 0, 21592, 7723188]\)	\(17394111071/411937500\)	\(-26364000000000000\)	\([2]\)	\(82944\)	\(1.8311\)