Elliptic curve isogeny class with Cremona label 133584k (LMFDB label 133584.cj)

• Label: 133584k
• Number of curves: $2$
• Conductor: $133584$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 133584k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 133584k do not have complex multiplication.

Modular form 133584.2.a.k

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 133584k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
133584.cj2	133584k1	\([0, 1, 0, -2944, 132020]\)	\(-389017/828\)	\(-6008227872768\)	\([2]\)	\(207360\)	\(1.1410\)	\(\Gamma_0(N)\)-optimal
133584.cj1	133584k2	\([0, 1, 0, -61024, 5777396]\)	\(3463512697/3174\)	\(23031540178944\)	\([2]\)	\(414720\)	\(1.4875\)