Elliptic curve isogeny class with Cremona label 97344dn (LMFDB label 97344.m)

• Label: 97344dn
• Number of curves: $2$
• Conductor: $97344$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 97344dn 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
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	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 97344dn do not have complex multiplication.

Modular form 97344.2.a.dn

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 97344dn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
97344.m2	97344dn1	\([0, 0, 0, 1716, 83824]\)	\(1331/8\)	\(-3358825906176\)	\([]\)	\(138240\)	\(1.0854\)	\(\Gamma_0(N)\)-optimal
97344.m1	97344dn2	\([0, 0, 0, -185484, -31260944]\)	\(-1680914269/32768\)	\(-13757750911696896\)	\([]\)	\(691200\)	\(1.8902\)