Elliptic curve isogeny class with LMFDB label 277440.ds (Cremona label 277440ds)

• Label: 277440.ds
• Number of curves: $4$
• Conductor: $277440$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 277440.ds have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 277440.ds do not have complex multiplication.

Modular form 277440.2.a.ds

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 277440.ds

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277440.ds1	277440ds4	\([0, -1, 0, -4624385, -1117577343]\)	\(6913728144004/3658971285\)	\(5788052479063239229440\)	\([2]\)	\(14155776\)	\(2.8673\)
277440.ds2	277440ds2	\([0, -1, 0, -2659185, 1656892017]\)	\(5258429611216/47403225\)	\(18746550096036249600\)	\([2, 2]\)	\(7077888\)	\(2.5208\)
277440.ds3	277440ds1	\([0, -1, 0, -2653405, 1664501965]\)	\(83587439220736/6885\)	\(170175654466560\)	\([2]\)	\(3538944\)	\(2.1742\)	\(\Gamma_0(N)\)-optimal
277440.ds4	277440ds3	\([0, -1, 0, -786465, 3944232225]\)	\(-34008619684/4228250625\)	\(-6688583923153674240000\)	\([2]\)	\(14155776\)	\(2.8673\)