Elliptic curve isogeny class with Cremona label 70070bg (LMFDB label 70070.bf)

• Label: 70070bg
• Number of curves: $2$
• Conductor: $70070$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 70070bg 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 70070.2.a.bg

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 70070bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
70070.bf2	70070bg1	\([1, 0, 0, 979, 10765]\)	\(881974079/929500\)	\(-109354745500\)	\([2]\)	\(82944\)	\(0.80487\)	\(\Gamma_0(N)\)-optimal
70070.bf1	70070bg2	\([1, 0, 0, -5391, 98671]\)	\(147281603041/49156250\)	\(5783183656250\)	\([2]\)	\(165888\)	\(1.1514\)