Elliptic curve isogeny class with LMFDB label 41280.cs (Cremona label 41280dl)

• Label: 41280.cs
• Number of curves: $4$
• Conductor: $41280$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 41280.cs have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 41280.cs do not have complex multiplication.

Modular form 41280.2.a.cs

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 41280.cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
41280.cs1	41280dl4	\([0, 1, 0, -1039265, -408129825]\)	\(947094050118111698/20769216075\)	\(2722262689382400\)	\([2]\)	\(655360\)	\(2.0774\)
41280.cs2	41280dl2	\([0, 1, 0, -67265, -5916225]\)	\(513591322675396/68238500625\)	\(4472078376960000\)	\([2, 2]\)	\(327680\)	\(1.7308\)
41280.cs3	41280dl1	\([0, 1, 0, -17265, 773775]\)	\(34739908901584/4081640625\)	\(66873600000000\)	\([2]\)	\(163840\)	\(1.3843\)	\(\Gamma_0(N)\)-optimal
41280.cs4	41280dl3	\([0, 1, 0, 104735, -31062625]\)	\(969360123836302/3748293231075\)	\(-491296290383462400\)	\([4]\)	\(655360\)	\(2.0774\)