Elliptic curve isogeny class with Cremona label 98736dj (LMFDB label 98736.dk)

• Label: 98736dj
• Number of curves: $4$
• Conductor: $98736$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 98736dj have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 8 T + 23 T^{2}\)	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 98736dj do not have complex multiplication.

Modular form 98736.2.a.dj

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 98736dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
98736.dk3	98736dj1	\([0, 1, 0, -16029152, -22230979212]\)	\(62768149033310713/6915442583808\)	\(50180621841258431643648\)	\([2]\)	\(11059200\)	\(3.0892\)	\(\Gamma_0(N)\)-optimal
98736.dk2	98736dj2	\([0, 1, 0, -60789472, 158582809460]\)	\(3423676911662954233/483711578981136\)	\(3509963032868455519420416\)	\([2, 2]\)	\(22118400\)	\(3.4358\)
98736.dk4	98736dj3	\([0, 1, 0, 99162848, 852455973620]\)	\(14861225463775641287/51859390496937804\)	\(-376308013826644512735412224\)	\([2]\)	\(44236800\)	\(3.7824\)
98736.dk1	98736dj4	\([0, 1, 0, -936906912, 11037508285428]\)	\(12534210458299016895673/315581882565708\)	\(2289961187164111790850048\)	\([4]\)	\(44236800\)	\(3.7824\)