Elliptic curve isogeny class with LMFDB label 386880.hg (Cremona label 386880hg)

• Label: 386880.hg
• Number of curves: $4$
• Conductor: $386880$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 386880.hg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 + T\)
\(31\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 386880.hg do not have complex multiplication.

Modular form 386880.2.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 LMFDB 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 LMFDB labels.

Elliptic curves in class 386880.hg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
386880.hg1	386880hg4	\([0, 1, 0, -23394465, 42939108063]\)	\(5401609226997647595049/86393158323264000\)	\(22647448095493718016000\)	\([2]\)	\(43794432\)	\(3.0895\)
386880.hg2	386880hg3	\([0, 1, 0, -2914465, -883995937]\)	\(10443846301537515049/4758933504000000\)	\(1247525864472576000000\)	\([2]\)	\(21897216\)	\(2.7430\)
386880.hg3	386880hg2	\([0, 1, 0, -2465505, -1463092065]\)	\(6322686217296773689/135260510172840\)	\(35457731178748968960\)	\([2]\)	\(14598144\)	\(2.5402\)
386880.hg4	386880hg1	\([0, 1, 0, -2452705, -1479299425]\)	\(6224721371657832889/2942222400\)	\(771285948825600\)	\([2]\)	\(7299072\)	\(2.1936\)	\(\Gamma_0(N)\)-optimal