Elliptic curve isogeny class with Cremona label 36432br (LMFDB label 36432.bf)

• Label: 36432br
• Number of curves: $2$
• Conductor: $36432$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 36432br have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 36432br do not have complex multiplication.

Modular form 36432.2.a.br

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 36432br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
36432.bf2	36432br1	\([0, 0, 0, 6045, -107678]\)	\(8181353375/6412032\)	\(-19146224959488\)	\([2]\)	\(73728\)	\(1.2366\)	\(\Gamma_0(N)\)-optimal
36432.bf1	36432br2	\([0, 0, 0, -28515, -930206]\)	\(858729462625/371764272\)	\(1110082167963648\)	\([2]\)	\(147456\)	\(1.5832\)