Elliptic curve isogeny class with LMFDB label 70070.bq (Cremona label 70070bd)

• Label: 70070.bq
• Number of curves: $4$
• Conductor: $70070$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 70070.bq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 70070.bq do not have complex multiplication.

Modular form 70070.2.a.bq

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 70070.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
70070.bq1	70070bd4	\([1, -1, 1, -723496108, -7490174313009]\)	\(355995140004443961140387841/2768480\)	\(325708903520\)	\([2]\)	\(10321920\)	\(3.2312\)
70070.bq2	70070bd3	\([1, -1, 1, -45320428, -116471371313]\)	\(87501897507774086005761/815991377947460000\)	\(96000569624140721540000\)	\([2]\)	\(10321920\)	\(3.2312\)
70070.bq3	70070bd2	\([1, -1, 1, -45218508, -117025489969]\)	\(86912881496074271306241/7664481510400\)	\(901718585217049600\)	\([2, 2]\)	\(5160960\)	\(2.8846\)
70070.bq4	70070bd1	\([1, -1, 1, -2819788, -1836647473]\)	\(-21075830718885163521/199306463150080\)	\(-23448206083143761920\)	\([2]\)	\(2580480\)	\(2.5380\)	\(\Gamma_0(N)\)-optimal