Elliptic curve isogeny class with Cremona label 80850ed (LMFDB label 80850.ee)

• Label: 80850ed
• Number of curves: $2$
• Conductor: $80850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 80850ed have rank \(1\).

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 \(\mathbb{F}_p\)
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 80850.2.a.ed

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 80850ed

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
80850.ee2	80850ed1	\([1, 1, 1, -142304688, 821579467281]\)	\(-59465789423385795028207/20003531867239219200\)	\(-107206428600985190400000000\)	\([2]\)	\(36771840\)	\(3.7067\)	\(\Gamma_0(N)\)-optimal
80850.ee1	80850ed2	\([1, 1, 1, -2436064688, 46274727627281]\)	\(298315634894429753085191407/22212303505611816960\)	\(119044064100388331520000000\)	\([2]\)	\(73543680\)	\(4.0532\)