Elliptic curve isogeny class with Cremona label 97344bq (LMFDB label 97344.ew)

• Label: 97344bq
• Number of curves: $4$
• Conductor: $97344$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 97344bq have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 97344.2.a.bq

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 97344bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
97344.ew4	97344bq1	\([0, 0, 0, -140439, -2891252]\)	\(1360251712/771147\)	\(173661996484087488\)	\([2]\)	\(1032192\)	\(1.9979\)	\(\Gamma_0(N)\)-optimal
97344.ew2	97344bq2	\([0, 0, 0, -1425684, 652069600]\)	\(22235451328/123201\)	\(1775668224405344256\)	\([2, 2]\)	\(2064384\)	\(2.3445\)
97344.ew3	97344bq3	\([0, 0, 0, -634764, 1371806800]\)	\(-245314376/6908733\)	\(-796592083440920592384\)	\([2]\)	\(4128768\)	\(2.6911\)
97344.ew1	97344bq4	\([0, 0, 0, -22780524, 41849826928]\)	\(11339065490696/351\)	\(40471070641717248\)	\([2]\)	\(4128768\)	\(2.6911\)