Elliptic curve isogeny class with Cremona label 145600bz (LMFDB label 145600.ew)

• Label: 145600bz
• Number of curves: $4$
• Conductor: $145600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 145600bz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 145600bz do not have complex multiplication.

Modular form 145600.2.a.bz

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 145600bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145600.ew3	145600bz1	\([0, 0, 0, -3200300, -2015998000]\)	\(884984855328729/83492864000\)	\(341986770944000000000\)	\([2]\)	\(4423680\)	\(2.6783\)	\(\Gamma_0(N)\)-optimal
145600.ew2	145600bz2	\([0, 0, 0, -11392300, 12549378000]\)	\(39920686684059609/6492304000000\)	\(26592477184000000000000\)	\([2, 2]\)	\(8847360\)	\(3.0248\)
145600.ew1	145600bz3	\([0, 0, 0, -174464300, 886941442000]\)	\(143378317900125424089/4976562500000\)	\(20384000000000000000000\)	\([2]\)	\(17694720\)	\(3.3714\)
145600.ew4	145600bz4	\([0, 0, 0, 20607700, 70341378000]\)	\(236293804275620391/658593925444000\)	\(-2697600718618624000000000\)	\([2]\)	\(17694720\)	\(3.3714\)