Elliptic curve isogeny class with Cremona label 273600pq (LMFDB label 273600.pq)

• Label: 273600pq
• Number of curves: $4$
• Conductor: $273600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 273600pq have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 273600pq do not have complex multiplication.

Modular form 273600.2.a.pq

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 273600pq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
273600.pq4	273600pq1	\([0, 0, 0, -144300, 36002000]\)	\(-111284641/123120\)	\(-367634350080000000\)	\([2]\)	\(3538944\)	\(2.0651\)	\(\Gamma_0(N)\)-optimal
273600.pq3	273600pq2	\([0, 0, 0, -2736300, 1741538000]\)	\(758800078561/324900\)	\(970146201600000000\)	\([2, 2]\)	\(7077888\)	\(2.4117\)
273600.pq1	273600pq3	\([0, 0, 0, -43776300, 111482498000]\)	\(3107086841064961/570\)	\(1702010880000000\)	\([2]\)	\(14155776\)	\(2.7583\)
273600.pq2	273600pq4	\([0, 0, 0, -3168300, 1154882000]\)	\(1177918188481/488703750\)	\(1459261578240000000000\)	\([2]\)	\(14155776\)	\(2.7583\)