Elliptic curve isogeny class with Cremona label 107712ch (LMFDB label 107712.ei)

• Label: 107712ch
• Number of curves: $4$
• Conductor: $107712$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 107712ch have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 107712ch do not have complex multiplication.

Modular form 107712.2.a.ch

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 107712ch

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
107712.ei3	107712ch1	\([0, 0, 0, -4769004, 3606865072]\)	\(62768149033310713/6915442583808\)	\(1321561658122838212608\)	\([2]\)	\(5898240\)	\(2.7861\)	\(\Gamma_0(N)\)-optimal
107712.ei2	107712ch2	\([0, 0, 0, -18086124, -25738740560]\)	\(3423676911662954233/483711578981136\)	\(92438722268954137460736\)	\([2, 2]\)	\(11796480\)	\(3.1327\)
107712.ei4	107712ch3	\([0, 0, 0, 29502996, -138334598480]\)	\(14861225463775641287/51859390496937804\)	\(-9910483857510933231304704\)	\([2]\)	\(23592960\)	\(3.4793\)
107712.ei1	107712ch4	\([0, 0, 0, -278749164, -1791261643088]\)	\(12534210458299016895673/315581882565708\)	\(60308636929989314347008\)	\([2]\)	\(23592960\)	\(3.4793\)