Elliptic curve isogeny class with Cremona label 47424cz (LMFDB label 47424.cc)

• Label: 47424cz
• Number of curves: $4$
• Conductor: $47424$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 47424cz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(13\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47424cz do not have complex multiplication.

Modular form 47424.2.a.cz

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 47424cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47424.cc3	47424cz1	\([0, 1, 0, -80029, 8687411]\)	\(55356847905445888/60021\)	\(61461504\)	\([2]\)	\(92160\)	\(1.2134\)	\(\Gamma_0(N)\)-optimal
47424.cc2	47424cz2	\([0, 1, 0, -80049, 8682831]\)	\(3462397543530448/3602520441\)	\(59023694905344\)	\([2, 2]\)	\(184320\)	\(1.5600\)
47424.cc4	47424cz3	\([0, 1, 0, -60609, 13025727]\)	\(-375718260235972/904469833683\)	\(-59275335020249088\)	\([2]\)	\(368640\)	\(1.9065\)
47424.cc1	47424cz4	\([0, 1, 0, -99809, 4047135]\)	\(1677865892403172/861235747047\)	\(56441945918472192\)	\([2]\)	\(368640\)	\(1.9065\)