Elliptic curve isogeny class with LMFDB label 206910.cy (Cremona label 206910be)

• Label: 206910.cy
• Number of curves: $4$
• Conductor: $206910$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 206910.cy have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 206910.cy do not have complex multiplication.

Modular form 206910.2.a.cy

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 206910.cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
206910.cy1	206910be3	\([1, -1, 1, -3310583, 2319315221]\)	\(3107086841064961/570\)	\(736136742330\)	\([2]\)	\(3932160\)	\(2.1128\)
206910.cy2	206910be4	\([1, -1, 1, -239603, 24077837]\)	\(1177918188481/488703750\)	\(631145239455183750\)	\([2]\)	\(3932160\)	\(2.1128\)
206910.cy3	206910be2	\([1, -1, 1, -206933, 36270281]\)	\(758800078561/324900\)	\(419597943128100\)	\([2, 2]\)	\(1966080\)	\(1.7662\)
206910.cy4	206910be1	\([1, -1, 1, -10913, 751457]\)	\(-111284641/123120\)	\(-159005536343280\)	\([2]\)	\(983040\)	\(1.4196\)	\(\Gamma_0(N)\)-optimal