Elliptic curve isogeny class with LMFDB label 385728.be (Cremona label 385728be)

• Label: 385728.be
• Number of curves: $4$
• Conductor: $385728$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 385728.be have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(41\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 385728.be do not have complex multiplication.

Modular form 385728.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 385728.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
385728.be1	385728be4	\([0, -1, 0, -6943169, -7039502847]\)	\(9601936036547336/3321\)	\(12802861596672\)	\([2]\)	\(5308416\)	\(2.3089\)
385728.be2	385728be3	\([0, -1, 0, -514369, -66247775]\)	\(3904008380936/1764915561\)	\(6803965569796964352\)	\([2]\)	\(5308416\)	\(2.3089\)
385728.be3	385728be2	\([0, -1, 0, -434009, -109851111]\)	\(18761723501248/11029041\)	\(5314787920318464\)	\([2, 2]\)	\(2654208\)	\(1.9623\)
385728.be4	385728be1	\([0, -1, 0, -22164, -2359566]\)	\(-159926162752/228886641\)	\(-1723410203328576\)	\([2]\)	\(1327104\)	\(1.6157\)	\(\Gamma_0(N)\)-optimal