Elliptic curve isogeny class with LMFDB label 162624.cf (Cremona label 162624hz)

• Label: 162624.cf
• Number of curves: $4$
• Conductor: $162624$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 162624.cf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 162624.cf do not have complex multiplication.

Modular form 162624.2.a.cf

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 162624.cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162624.cf1	162624hz4	\([0, -1, 0, -884913, 320699601]\)	\(2640279346000/3087\)	\(89600963493888\)	\([2]\)	\(1244160\)	\(1.9603\)
162624.cf2	162624hz3	\([0, -1, 0, -54853, 5110789]\)	\(-10061824000/352947\)	\(-640273551633408\)	\([2]\)	\(622080\)	\(1.6138\)
162624.cf3	162624hz2	\([0, -1, 0, -13713, 202545]\)	\(9826000/5103\)	\(148115878428672\)	\([2]\)	\(414720\)	\(1.4110\)
162624.cf4	162624hz1	\([0, -1, 0, 3227, 22981]\)	\(2048000/1323\)	\(-2400025807872\)	\([2]\)	\(207360\)	\(1.0645\)	\(\Gamma_0(N)\)-optimal