Elliptic curve isogeny class with Cremona label 80850el (LMFDB label 80850.ez)

• Label: 80850el
• Number of curves: $4$
• Conductor: $80850$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 80850el have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 80850el do not have complex multiplication.

Modular form 80850.2.a.el

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 80850el

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
80850.ez4	80850el1	\([1, 1, 1, 4262, 67031]\)	\(4657463/3696\)	\(-6794229750000\)	\([2]\)	\(196608\)	\(1.1502\)	\(\Gamma_0(N)\)-optimal
80850.ez3	80850el2	\([1, 1, 1, -20238, 557031]\)	\(498677257/213444\)	\(392366768062500\)	\([2, 2]\)	\(393216\)	\(1.4968\)
80850.ez2	80850el3	\([1, 1, 1, -154988, -23158969]\)	\(223980311017/4278582\)	\(7865170214343750\)	\([2]\)	\(786432\)	\(1.8433\)
80850.ez1	80850el4	\([1, 1, 1, -277488, 56123031]\)	\(1285429208617/614922\)	\(1130389974656250\)	\([2]\)	\(786432\)	\(1.8433\)