Elliptic curve isogeny class with Cremona label 97344dg (LMFDB label 97344.bh)

• Label: 97344dg
• Number of curves: $4$
• Conductor: $97344$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 97344dg have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 97344dg do not have complex multiplication.

Modular form 97344.2.a.dg

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 97344dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
97344.bh4	97344dg1	\([0, 0, 0, 27924, 743600]\)	\(5735339/3888\)	\(-1632389390401536\)	\([2]\)	\(368640\)	\(1.6077\)	\(\Gamma_0(N)\)-optimal
97344.bh3	97344dg2	\([0, 0, 0, -121836, 6194864]\)	\(476379541/236196\)	\(99167655466893312\)	\([2]\)	\(737280\)	\(1.9543\)
97344.bh2	97344dg3	\([0, 0, 0, -2555436, -1573308880]\)	\(-4395631034341/3145728\)	\(-1320744087522902016\)	\([2]\)	\(1843200\)	\(2.4125\)
97344.bh1	97344dg4	\([0, 0, 0, -40893996, -100655483344]\)	\(18013780041269221/9216\)	\(3869367443914752\)	\([2]\)	\(3686400\)	\(2.7590\)