Elliptic curve isogeny class with LMFDB label 133584.dr (Cremona label 133584ba)

• Label: 133584.dr
• Number of curves: $4$
• Conductor: $133584$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 133584.dr 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.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 133584.2.a.dr

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 133584.dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
133584.dr1	133584ba3	\([0, 1, 0, -478232, 127114260]\)	\(1666957239793/301806\)	\(2189999059623936\)	\([2]\)	\(1105920\)	\(1.9471\)
133584.dr2	133584ba4	\([0, 1, 0, -207192, -35184492]\)	\(135559106353/5037138\)	\(36551054263984128\)	\([2]\)	\(1105920\)	\(1.9471\)
133584.dr3	133584ba2	\([0, 1, 0, -32952, 1545300]\)	\(545338513/171396\)	\(1243703169662976\)	\([2, 2]\)	\(552960\)	\(1.6005\)
133584.dr4	133584ba1	\([0, 1, 0, 5768, 166868]\)	\(2924207/3312\)	\(-24032911491072\)	\([2]\)	\(276480\)	\(1.2540\)	\(\Gamma_0(N)\)-optimal