Elliptic curve isogeny class with Cremona label 91728el (LMFDB label 91728.bg)

• Label: 91728el
• Number of curves: $4$
• Conductor: $91728$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 91728el have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	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 91728el do not have complex multiplication.

Modular form 91728.2.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 91728el

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91728.bg3	91728el1	\([0, 0, 0, -398811, 94263946]\)	\(19968681097/628992\)	\(220963651502211072\)	\([2]\)	\(884736\)	\(2.1029\)	\(\Gamma_0(N)\)-optimal
91728.bg2	91728el2	\([0, 0, 0, -963291, -232118390]\)	\(281397674377/96589584\)	\(33931730733808287744\)	\([2, 2]\)	\(1769472\)	\(2.4495\)
91728.bg4	91728el3	\([0, 0, 0, 2846949, -1613711414]\)	\(7264187703863/7406095788\)	\(-2601746872283948433408\)	\([2]\)	\(3538944\)	\(2.7961\)
91728.bg1	91728el4	\([0, 0, 0, -13805211, -19738994870]\)	\(828279937799497/193444524\)	\(67956680508094070784\)	\([2]\)	\(3538944\)	\(2.7961\)