Elliptic curve isogeny class with LMFDB label 432.b (Cremona label 432f)

• Label: 432.b
• Number of curves: $3$
• Conductor: $432$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 432.b have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 432.b do not have complex multiplication.

Modular form 432.2.a.b

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 432.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
432.b1	432f3	\([0, 0, 0, -459, 3834]\)	\(-132651/2\)	\(-161243136\)	\([]\)	\(144\)	\(0.37794\)
432.b2	432f2	\([0, 0, 0, -219, -1654]\)	\(-1167051/512\)	\(-509607936\)	\([]\)	\(144\)	\(0.37794\)
432.b3	432f1	\([0, 0, 0, 21, 26]\)	\(9261/8\)	\(-884736\)	\([]\)	\(48\)	\(-0.17136\)	\(\Gamma_0(N)\)-optimal