Elliptic curve isogeny class with Cremona label 112530dg (LMFDB label 112530.cy)

• Label: 112530dg
• Number of curves: $2$
• Conductor: $112530$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 112530dg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 112530dg do not have complex multiplication.

Modular form 112530.2.a.dg

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 112530dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
112530.cy2	112530dg1	\([1, 0, 0, -1651350, -818095068]\)	\(-281115640967896441/468084326400\)	\(-829239937361510400\)	\([2]\)	\(2912000\)	\(2.3341\)	\(\Gamma_0(N)\)-optimal
112530.cy1	112530dg2	\([1, 0, 0, -26432150, -52307641308]\)	\(1152829477932246539641/3188367360\)	\(5648387268648960\)	\([2]\)	\(5824000\)	\(2.6807\)