Elliptic curve isogeny class with Cremona label 133560bh (LMFDB label 133560.o)

• Label: 133560bh
• Number of curves: $2$
• Conductor: $133560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 133560bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(53\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 133560bh do not have complex multiplication.

Modular form 133560.2.a.bh

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 133560bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
133560.o2	133560bh1	\([0, 0, 0, -363, -18538]\)	\(-7086244/194775\)	\(-145398758400\)	\([2]\)	\(122880\)	\(0.82242\)	\(\Gamma_0(N)\)-optimal
133560.o1	133560bh2	\([0, 0, 0, -12963, -565378]\)	\(161355136322/884835\)	\(1321051576320\)	\([2]\)	\(245760\)	\(1.1690\)