Elliptic curve isogeny class with Cremona label 277200nw (LMFDB label 277200.nw)

• Label: 277200nw
• Number of curves: $4$
• Conductor: $277200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 277200nw have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 277200nw do not have complex multiplication.

Modular form 277200.2.a.nw

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 277200nw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277200.nw3	277200nw1	\([0, 0, 0, -3108675, -2105410750]\)	\(71210194441849/165580800\)	\(7725337804800000000\)	\([2]\)	\(7077888\)	\(2.5048\)	\(\Gamma_0(N)\)-optimal
277200.nw2	277200nw2	\([0, 0, 0, -4260675, -403906750]\)	\(183337554283129/104587560000\)	\(4879637199360000000000\)	\([2, 2]\)	\(14155776\)	\(2.8514\)
277200.nw1	277200nw3	\([0, 0, 0, -43860675, 111307693250]\)	\(200005594092187129/1027287538200\)	\(47929127382259200000000\)	\([2]\)	\(28311552\)	\(3.1980\)
277200.nw4	277200nw4	\([0, 0, 0, 16907325, -3219250750]\)	\(11456208593737991/6725709375000\)	\(-313794696600000000000000\)	\([2]\)	\(28311552\)	\(3.1980\)