Elliptic curve isogeny class with Cremona label 130050hg (LMFDB label 130050.db)

• Label: 130050hg
• Number of curves: $4$
• Conductor: $130050$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 130050hg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 130050hg do not have complex multiplication.

Modular form 130050.2.a.hg

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 130050hg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
130050.db3	130050hg1	\([1, -1, 0, -55542, 5752116]\)	\(-1860867/320\)	\(-3258571815000000\)	\([2]\)	\(884736\)	\(1.7030\)	\(\Gamma_0(N)\)-optimal
130050.db2	130050hg2	\([1, -1, 0, -922542, 341281116]\)	\(8527173507/200\)	\(2036607384375000\)	\([2]\)	\(1769472\)	\(2.0495\)
130050.db4	130050hg3	\([1, -1, 0, 377958, -24448384]\)	\(804357/500\)	\(-3711716958023437500\)	\([2]\)	\(2654208\)	\(2.2523\)
130050.db1	130050hg4	\([1, -1, 0, -1572792, -198065134]\)	\(57960603/31250\)	\(231982309876464843750\)	\([2]\)	\(5308416\)	\(2.5988\)