Elliptic curve isogeny class with Cremona label 37440dq (LMFDB label 37440.bk)

• Label: 37440dq
• Number of curves: $4$
• Conductor: $37440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 37440dq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 37440dq do not have complex multiplication.

Modular form 37440.2.a.dq

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 37440dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37440.bk4	37440dq1	\([0, 0, 0, 6072, 12152]\)	\(33165879296/19278675\)	\(-14391453772800\)	\([2]\)	\(49152\)	\(1.2142\)	\(\Gamma_0(N)\)-optimal
37440.bk3	37440dq2	\([0, 0, 0, -24348, 97328]\)	\(133649126224/77000625\)	\(919690536960000\)	\([2, 2]\)	\(98304\)	\(1.5608\)
37440.bk2	37440dq3	\([0, 0, 0, -258348, -50353072]\)	\(39914580075556/172718325\)	\(8251746479308800\)	\([2]\)	\(196608\)	\(1.9074\)
37440.bk1	37440dq4	\([0, 0, 0, -277068, 55998992]\)	\(49235161015876/137109375\)	\(6550502400000000\)	\([2]\)	\(196608\)	\(1.9074\)