Elliptic curve isogeny class with Cremona label 98736bj (LMFDB label 98736.dn)

• Label: 98736bj
• Number of curves: $2$
• Conductor: $98736$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 98736bj have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

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
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 98736bj do not have complex multiplication.

Modular form 98736.2.a.bj

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 98736bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
98736.dn1	98736bj1	\([0, 1, 0, -9236, 160092]\)	\(192143824/85833\)	\(38926949200128\)	\([2]\)	\(460800\)	\(1.3032\)	\(\Gamma_0(N)\)-optimal
98736.dn2	98736bj2	\([0, 1, 0, 31904, 1229732]\)	\(1979654684/1499553\)	\(-2720306802926592\)	\([2]\)	\(921600\)	\(1.6498\)