Elliptic curve isogeny class with LMFDB label 112710.bl (Cremona label 112710bi)

• Label: 112710.bl
• Number of curves: $4$
• Conductor: $112710$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 112710.bl have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 112710.2.a.bl

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 112710.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
112710.bl1	112710bi4	\([1, 0, 1, -139738, -20113702]\)	\(12501706118329/2570490\)	\(62045379738810\)	\([2]\)	\(589824\)	\(1.6436\)
112710.bl2	112710bi2	\([1, 0, 1, -9688, -242062]\)	\(4165509529/1368900\)	\(33041918204100\)	\([2, 2]\)	\(294912\)	\(1.2971\)
112710.bl3	112710bi1	\([1, 0, 1, -3908, 90866]\)	\(273359449/9360\)	\(225927645840\)	\([2]\)	\(147456\)	\(0.95049\)	\(\Gamma_0(N)\)-optimal
112710.bl4	112710bi3	\([1, 0, 1, 27882, -1654694]\)	\(99317171591/106616250\)	\(-2573457090896250\)	\([2]\)	\(589824\)	\(1.6436\)