Elliptic curve isogeny class with Cremona label 37440ff (LMFDB label 37440.fs)

• Label: 37440ff
• Number of curves: $4$
• Conductor: $37440$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 37440ff have rank \(0\).

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.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 37440.2.a.ff

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 37440ff

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37440.fs4	37440ff1	\([0, 0, 0, 117393, 11012056]\)	\(3834800837445824/3342041015625\)	\(-155926265625000000\)	\([2]\)	\(393216\)	\(1.9865\)	\(\Gamma_0(N)\)-optimal
37440.fs3	37440ff2	\([0, 0, 0, -585732, 97637056]\)	\(7442744143086784/2927948765625\)	\(8742808166976000000\)	\([2, 2]\)	\(786432\)	\(2.3331\)
37440.fs2	37440ff3	\([0, 0, 0, -4230732, -3280548944]\)	\(350584567631475848/8259273550125\)	\(197296469378371584000\)	\([2]\)	\(1572864\)	\(2.6797\)
37440.fs1	37440ff4	\([0, 0, 0, -8190732, 9019823056]\)	\(2543984126301795848/909361981125\)	\(21722722606780416000\)	\([2]\)	\(1572864\)	\(2.6797\)