Elliptic curve isogeny class with Cremona label 54720el (LMFDB label 54720.ei)

• Label: 54720el
• Number of curves: $4$
• Conductor: $54720$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 54720el have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 23 T^{2}\)	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 54720el do not have complex multiplication.

Modular form 54720.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 54720el

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54720.ei4	54720el1	\([0, 0, 0, 5376948, -10204336496]\)	\(89962967236397039/287450726400000\)	\(-54932689268401766400000\)	\([2]\)	\(3686400\)	\(3.0466\)	\(\Gamma_0(N)\)-optimal
54720.ei3	54720el2	\([0, 0, 0, -50656332, -119558885744]\)	\(75224183150104868881/11219310000000000\)	\(2144043529666560000000000\)	\([2]\)	\(7372800\)	\(3.3931\)
54720.ei2	54720el3	\([0, 0, 0, -1901643852, -31918467238256]\)	\(-3979640234041473454886161/1471455901872240\)	\(-281199601900549035786240\)	\([2]\)	\(18432000\)	\(3.8513\)
54720.ei1	54720el4	\([0, 0, 0, -30426304332, -2042781522572144]\)	\(16300610738133468173382620881/2228489100\)	\(425870898993561600\)	\([2]\)	\(36864000\)	\(4.1979\)