Elliptic curve isogeny class with Cremona label 115600cz (LMFDB label 115600.bj)

• Label: 115600cz
• Number of curves: $2$
• Conductor: $115600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 115600cz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 115600cz do not have complex multiplication.

Modular form 115600.2.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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 115600cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
115600.bj1	115600cz1	\([0, -1, 0, -1678608, 839326912]\)	\(-1723025/4\)	\(-1214339855329280000\)	\([]\)	\(1566720\)	\(2.3509\)	\(\Gamma_0(N)\)-optimal
115600.bj2	115600cz2	\([0, -1, 0, 12077792, -13742457088]\)	\(1026895/1024\)	\(-194294376852684800000000\)	\([]\)	\(7833600\)	\(3.1556\)