Elliptic curve isogeny class with Cremona label 32634bz (LMFDB label 32634.bk)

• Label: 32634bz
• Number of curves: $2$
• Conductor: $32634$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 32634bz have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32634bz do not have complex multiplication.

Modular form 32634.2.a.bz

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 32634bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32634.bk2	32634bz1	\([1, -1, 1, 73858, -226002675]\)	\(519524563319/257532162048\)	\(-22087534571600375808\)	\([2]\)	\(1474560\)	\(2.3909\)	\(\Gamma_0(N)\)-optimal
32634.bk1	32634bz2	\([1, -1, 1, -5147582, -4382268915]\)	\(175880497476668041/4994797131072\)	\(428384375113974011712\)	\([2]\)	\(2949120\)	\(2.7374\)