Elliptic curve isogeny class with Cremona label 158400dq (LMFDB label 158400.hw)

• Label: 158400dq
• Number of curves: $6$
• Conductor: $158400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 158400dq have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 158400dq do not have complex multiplication.

Modular form 158400.2.a.dq

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 158400dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158400.hw5	158400dq1	\([0, 0, 0, -157800, 40327000]\)	\(-37256083456/38671875\)	\(-451068750000000000\)	\([2]\)	\(1572864\)	\(2.0828\)	\(\Gamma_0(N)\)-optimal
158400.hw4	158400dq2	\([0, 0, 0, -2970300, 1969702000]\)	\(15529488955216/6125625\)	\(1143188640000000000\)	\([2, 2]\)	\(3145728\)	\(2.4294\)
158400.hw1	158400dq3	\([0, 0, 0, -47520300, 126086002000]\)	\(15897679904620804/2475\)	\(1847577600000000\)	\([2]\)	\(6291456\)	\(2.7760\)
158400.hw3	158400dq4	\([0, 0, 0, -3420300, 1333402000]\)	\(5927735656804/2401490025\)	\(1792702697702400000000\)	\([2, 2]\)	\(6291456\)	\(2.7760\)
158400.hw6	158400dq5	\([0, 0, 0, 11159700, 9702322000]\)	\(102949393183198/86815346805\)	\(-129614618257090560000000\)	\([2]\)	\(12582912\)	\(3.1226\)
158400.hw2	158400dq6	\([0, 0, 0, -25200300, -47758718000]\)	\(1185450336504002/26043266205\)	\(38882388097935360000000\)	\([2]\)	\(12582912\)	\(3.1226\)