Elliptic curve isogeny class with Cremona label 69696bk (LMFDB label 69696.eg)

• Label: 69696bk
• Number of curves: $2$
• Conductor: $69696$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 69696bk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)

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.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 69696bk do not have complex multiplication.

Modular form 69696.2.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 69696bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
69696.eg1	69696bk1	\([0, 0, 0, -428340, 107885536]\)	\(1643032000/297\)	\(1571086281904128\)	\([2]\)	\(368640\)	\(1.9195\)	\(\Gamma_0(N)\)-optimal
69696.eg2	69696bk2	\([0, 0, 0, -384780, 130693552]\)	\(-148877000/88209\)	\(-3732901005804208128\)	\([2]\)	\(737280\)	\(2.2661\)