Elliptic curve isogeny class with Cremona label 315810dx (LMFDB label 315810.dx)

• Label: 315810dx
• Number of curves: $2$
• Conductor: $315810$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 315810dx have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 315810dx do not have complex multiplication.

Modular form 315810.2.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 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 315810dx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
315810.dx2	315810dx1	\([1, -1, 1, -30152, 1563851]\)	\(63378025803/14801600\)	\(707992307035200\)	\([2]\)	\(1290240\)	\(1.5613\)	\(\Gamma_0(N)\)-optimal
315810.dx1	315810dx2	\([1, -1, 1, -451232, 116771339]\)	\(212423523093963/17545000\)	\(839215019115000\)	\([2]\)	\(2580480\)	\(1.9079\)