Elliptic curve isogeny class with Cremona label 42432y (LMFDB label 42432.cl)

• Label: 42432y
• Number of curves: $2$
• Conductor: $42432$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 42432y have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(13\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 42432y do not have complex multiplication.

Modular form 42432.2.a.y

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 42432y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42432.cl1	42432y1	\([0, 1, 0, -4037, 69483]\)	\(7107347955712/1996623837\)	\(2044542809088\)	\([2]\)	\(55296\)	\(1.0692\)	\(\Gamma_0(N)\)-optimal
42432.cl2	42432y2	\([0, 1, 0, 10543, 468975]\)	\(7909612346288/10289870721\)	\(-168589241892864\)	\([2]\)	\(110592\)	\(1.4158\)