Elliptic curve isogeny class with Cremona label 356928cz (LMFDB label 356928.cz)

• Label: 356928cz
• Number of curves: $4$
• Conductor: $356928$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 356928cz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	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 356928cz do not have complex multiplication.

Modular form 356928.2.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 356928cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
356928.cz4	356928cz1	\([0, -1, 0, -879532, 252384118]\)	\(243578556889408/52089208083\)	\(16091178136185417408\)	\([2]\)	\(8847360\)	\(2.3997\)	\(\Gamma_0(N)\)-optimal
356928.cz2	356928cz2	\([0, -1, 0, -13251177, 18569841705]\)	\(13015685560572352/864536409\)	\(17092411882655256576\)	\([2, 2]\)	\(17694720\)	\(2.7463\)
356928.cz1	356928cz3	\([0, -1, 0, -212015457, 1188297629505]\)	\(6663712298552914184/29403\)	\(4650521887604736\)	\([2]\)	\(35389440\)	\(3.0928\)
356928.cz3	356928cz4	\([0, -1, 0, -12433217, 20961393153]\)	\(-1343891598641864/421900912521\)	\(-66729906066704809623552\)	\([2]\)	\(35389440\)	\(3.0928\)