Elliptic curve isogeny class with Cremona label 107712bk (LMFDB label 107712.do)

• Label: 107712bk
• Number of curves: $2$
• Conductor: $107712$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 107712bk have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 107712.2.a.bk

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 107712bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
107712.do2	107712bk1	\([0, 0, 0, -152364, 1131568]\)	\(2046931732873/1181672448\)	\(225821121470005248\)	\([2]\)	\(737280\)	\(2.0194\)	\(\Gamma_0(N)\)-optimal
107712.do1	107712bk2	\([0, 0, 0, -1719084, 865334320]\)	\(2940001530995593/8673562656\)	\(1657543636084064256\)	\([2]\)	\(1474560\)	\(2.3660\)