Elliptic curve isogeny class with LMFDB label 332592.be (Cremona label 332592be)

• Label: 332592.be
• Number of curves: $4$
• Conductor: $332592$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 332592.be have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(13\)	\(1\)
\(41\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	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 332592.be do not have complex multiplication.

Modular form 332592.2.a.be

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 332592.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
332592.be1	332592be3	\([0, -1, 0, -1187112, 498206448]\)	\(9357915116017/538002\)	\(10636627540451328\)	\([2]\)	\(5308416\)	\(2.1388\)
332592.be2	332592be2	\([0, -1, 0, -78472, 6857200]\)	\(2703045457/544644\)	\(10767943929839616\)	\([2, 2]\)	\(2654208\)	\(1.7922\)
332592.be3	332592be1	\([0, -1, 0, -24392, -1362960]\)	\(81182737/5904\)	\(116725679456256\)	\([2]\)	\(1327104\)	\(1.4456\)	\(\Gamma_0(N)\)-optimal
332592.be4	332592be4	\([0, -1, 0, 164888, 40732912]\)	\(25076571983/50863698\)	\(-1005606319225577472\)	\([2]\)	\(5308416\)	\(2.1388\)