Elliptic curve isogeny class with LMFDB label 37440.cp (Cremona label 37440dz)

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

Rank

The elliptic curves in class 37440.cp 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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 37440.2.a.cp

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 37440.cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37440.cp1	37440dz4	\([0, 0, 0, -59628, -5583152]\)	\(490757540836/2142075\)	\(102339226828800\)	\([2]\)	\(196608\)	\(1.5412\)
37440.cp2	37440dz2	\([0, 0, 0, -5628, 11248]\)	\(1650587344/950625\)	\(11354204160000\)	\([2, 2]\)	\(98304\)	\(1.1946\)
37440.cp3	37440dz1	\([0, 0, 0, -4008, 97432]\)	\(9538484224/26325\)	\(19651507200\)	\([2]\)	\(49152\)	\(0.84805\)	\(\Gamma_0(N)\)-optimal
37440.cp4	37440dz3	\([0, 0, 0, 22452, 89872]\)	\(26198797244/15234375\)	\(-727833600000000\)	\([2]\)	\(196608\)	\(1.5412\)