Elliptic curve isogeny class with LMFDB label 262080.gp (Cremona label 262080gp)

• Label: 262080.gp
• Number of curves: $4$
• Conductor: $262080$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 262080.gp have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 262080.gp do not have complex multiplication.

Modular form 262080.2.a.gp

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 262080.gp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
262080.gp1	262080gp3	\([0, 0, 0, -62807148, 191579351472]\)	\(143378317900125424089/4976562500000\)	\(951035904000000000000\)	\([2]\)	\(23592960\)	\(3.1160\)
262080.gp2	262080gp2	\([0, 0, 0, -4101228, 2710665648]\)	\(39920686684059609/6492304000000\)	\(1240698615496704000000\)	\([2, 2]\)	\(11796480\)	\(2.7694\)
262080.gp3	262080gp1	\([0, 0, 0, -1152108, -435455568]\)	\(884984855328729/83492864000\)	\(15955734785163264000\)	\([2]\)	\(5898240\)	\(2.4228\)	\(\Gamma_0(N)\)-optimal
262080.gp4	262080gp4	\([0, 0, 0, 7418772, 15193737648]\)	\(236293804275620391/658593925444000\)	\(-125859259127870521344000\)	\([2]\)	\(23592960\)	\(3.1160\)