Elliptic curve isogeny class with Cremona label 69696s (LMFDB label 69696.k)

• Label: 69696s
• Number of curves: $2$
• Conductor: $69696$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 69696s have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 69696.2.a.s

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 69696s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
69696.k2	69696s1	\([0, 0, 0, -117612, -2874960]\)	\(19683/11\)	\(100549522041864192\)	\([2]\)	\(737280\)	\(1.9527\)	\(\Gamma_0(N)\)-optimal
69696.k1	69696s2	\([0, 0, 0, -1163052, 480118320]\)	\(19034163/121\)	\(1106044742460506112\)	\([2]\)	\(1474560\)	\(2.2993\)