Elliptic curve isogeny class with LMFDB label 2064.e (Cremona label 2064i)

• Label: 2064.e
• Number of curves: $4$
• Conductor: $2064$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 2064.e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2064.e do not have complex multiplication.

Modular form 2064.2.a.e

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 LMFDB 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 LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 2064.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2064.e1	2064i3	\([0, -1, 0, -3912, -91728]\)	\(1616855892553/22851963\)	\(93601640448\)	\([2]\)	\(1920\)	\(0.90997\)
2064.e2	2064i2	\([0, -1, 0, -472, 1840]\)	\(2845178713/1347921\)	\(5521084416\)	\([2, 2]\)	\(960\)	\(0.56340\)
2064.e3	2064i1	\([0, -1, 0, -392, 3120]\)	\(1630532233/1161\)	\(4755456\)	\([2]\)	\(480\)	\(0.21683\)	\(\Gamma_0(N)\)-optimal
2064.e4	2064i4	\([0, -1, 0, 1688, 12208]\)	\(129784785047/92307627\)	\(-378092040192\)	\([4]\)	\(1920\)	\(0.90997\)