Elliptic curve isogeny class with LMFDB label 88200.dq (Cremona label 88200cb)

• Label: 88200.dq
• Number of curves: $4$
• Conductor: $88200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 88200.dq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 88200.dq do not have complex multiplication.

Modular form 88200.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 88200.dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
88200.dq1	88200cb4	\([0, 0, 0, -2385075, -1416847250]\)	\(546718898/405\)	\(1111528928160000000\)	\([2]\)	\(1769472\)	\(2.3964\)
88200.dq2	88200cb3	\([0, 0, 0, -1503075, 700834750]\)	\(136835858/1875\)	\(5145967260000000000\)	\([2]\)	\(1769472\)	\(2.3964\)
88200.dq3	88200cb2	\([0, 0, 0, -180075, -12262250]\)	\(470596/225\)	\(308758035600000000\)	\([2, 2]\)	\(884736\)	\(2.0498\)
88200.dq4	88200cb1	\([0, 0, 0, 40425, -1457750]\)	\(21296/15\)	\(-5145967260000000\)	\([2]\)	\(442368\)	\(1.7032\)	\(\Gamma_0(N)\)-optimal