Elliptic curve isogeny class with Cremona label 203280dq (LMFDB label 203280.cb)

• Label: 203280dq
• Number of curves: $4$
• Conductor: $203280$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 203280dq have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 203280dq do not have complex multiplication.

Modular form 203280.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 203280dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
203280.cb3	203280dq1	\([0, -1, 0, -621496, -143945360]\)	\(3658671062929/880165440\)	\(6386756677844336640\)	\([2]\)	\(4976640\)	\(2.3195\)	\(\Gamma_0(N)\)-optimal
203280.cb4	203280dq2	\([0, -1, 0, 1469384, -906698384]\)	\(48351870250991/76871856600\)	\(-557806318183025049600\)	\([2]\)	\(9953280\)	\(2.6661\)
203280.cb1	203280dq3	\([0, -1, 0, -46969336, -123883896464]\)	\(1579250141304807889/41926500\)	\(304231842883584000\)	\([2]\)	\(14929920\)	\(2.8688\)
203280.cb2	203280dq4	\([0, -1, 0, -46911256, -124205613200]\)	\(-1573398910560073969/8138108343750\)	\(-59052668336382336000000\)	\([2]\)	\(29859840\)	\(3.2154\)