Elliptic curve isogeny class with LMFDB label 359856.dx (Cremona label 359856dx)

• Label: 359856.dx
• Number of curves: $3$
• Conductor: $359856$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 359856.dx have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 359856.dx do not have complex multiplication.

Modular form 359856.2.a.dx

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 359856.dx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
359856.dx1	359856dx3	\([0, 0, 0, -1249758720, -17005420566288]\)	\(22759502184972288000/5831\)	\(55307308203528192\)	\([]\)	\(51508224\)	\(3.4950\)
359856.dx2	359856dx2	\([0, 0, 0, -96126240, 347223394672]\)	\(838870874148864000/40675641638471\)	\(4763090947437557133299712\)	\([]\)	\(51508224\)	\(3.4950\)
359856.dx3	359856dx1	\([0, 0, 0, -15452640, -23252365136]\)	\(31363160518656000/198257271191\)	\(2579532930479918665728\)	\([]\)	\(17169408\)	\(2.9457\)	\(\Gamma_0(N)\)-optimal