Elliptic curve isogeny class with Cremona label 112710ci (LMFDB label 112710.cb)

• Label: 112710ci
• Number of curves: $4$
• Conductor: $112710$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 112710ci have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 112710ci do not have complex multiplication.

Modular form 112710.2.a.ci

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 112710ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
112710.cb3	112710ci1	\([1, 1, 1, -1740, 178605]\)	\(-24137569/561600\)	\(-13555658750400\)	\([2]\)	\(248832\)	\(1.2006\)	\(\Gamma_0(N)\)-optimal
112710.cb2	112710ci2	\([1, 1, 1, -59540, 5542445]\)	\(967068262369/4928040\)	\(118950905534760\)	\([2]\)	\(497664\)	\(1.5471\)
112710.cb4	112710ci3	\([1, 1, 1, 15600, -4732083]\)	\(17394111071/411937500\)	\(-9943169829937500\)	\([2]\)	\(746496\)	\(1.7499\)
112710.cb1	112710ci4	\([1, 1, 1, -345650, -74381083]\)	\(189208196468929/10860320250\)	\(262141729396472250\)	\([2]\)	\(1492992\)	\(2.0964\)