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

• Label: 262080ec
• Number of curves: $4$
• Conductor: $262080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 262080ec have rank \(1\).

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.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 262080.2.a.ec

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 262080ec

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
262080.ec4	262080ec1	\([0, 0, 0, -16428, 188368]\)	\(2565726409/1404585\)	\(268420373544960\)	\([2]\)	\(1048576\)	\(1.4594\)	\(\Gamma_0(N)\)-optimal
262080.ec2	262080ec2	\([0, 0, 0, -157548, -23914928]\)	\(2263054145689/16769025\)	\(3204610582118400\)	\([2, 2]\)	\(2097152\)	\(1.8059\)
262080.ec3	262080ec3	\([0, 0, 0, -56748, -54114608]\)	\(-105756712489/6558605235\)	\(-1253368978817679360\)	\([2]\)	\(4194304\)	\(2.1525\)
262080.ec1	262080ec4	\([0, 0, 0, -2516268, -1536326192]\)	\(9219915604149769/511875\)	\(97820835840000\)	\([2]\)	\(4194304\)	\(2.1525\)