Elliptic curve isogeny class with Cremona label 267696dl (LMFDB label 267696.dl)

• Label: 267696dl
• Number of curves: $4$
• Conductor: $267696$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 267696dl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 267696dl do not have complex multiplication.

Modular form 267696.2.a.dl

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 267696dl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
267696.dl4	267696dl1	\([0, 0, 0, -174915, -27150526]\)	\(1108717875/45056\)	\(24051183903571968\)	\([2]\)	\(1769472\)	\(1.9091\)	\(\Gamma_0(N)\)-optimal
267696.dl2	267696dl2	\([0, 0, 0, -2770755, -1775189182]\)	\(4406910829875/7744\)	\(4133797233426432\)	\([2]\)	\(3538944\)	\(2.2557\)
267696.dl3	267696dl3	\([0, 0, 0, -2121795, 1181515842]\)	\(2714704875/21296\)	\(8287230003711639552\)	\([2]\)	\(5308416\)	\(2.4584\)
267696.dl1	267696dl4	\([0, 0, 0, -3581955, -652153086]\)	\(13060888875/7086244\)	\(2757575783735048060928\)	\([2]\)	\(10616832\)	\(2.8050\)