Elliptic curve isogeny class with Cremona label 98736by (LMFDB label 98736.ca)

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

Rank

The elliptic curves in class 98736by 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
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 8 T + 23 T^{2}\)	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 98736by do not have complex multiplication.

Modular form 98736.2.a.by

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 98736by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
98736.ca4	98736by1	\([0, -1, 0, -11319832, -11459927312]\)	\(22106889268753393/4969545596928\)	\(36060582573012437434368\)	\([2]\)	\(7741440\)	\(3.0412\)	\(\Gamma_0(N)\)-optimal
98736.ca2	98736by2	\([0, -1, 0, -169916952, -852405296400]\)	\(74768347616680342513/5615307472896\)	\(40746433421275589246976\)	\([2, 2]\)	\(15482880\)	\(3.3878\)
98736.ca3	98736by3	\([0, -1, 0, -158765592, -969128811792]\)	\(-60992553706117024753/20624795251201152\)	\(-149659987558453919900762112\)	\([2]\)	\(30965760\)	\(3.7344\)
98736.ca1	98736by4	\([0, -1, 0, -2718622232, -54558722956560]\)	\(306234591284035366263793/1727485056\)	\(12535173747885735936\)	\([2]\)	\(30965760\)	\(3.7344\)