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

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

Rank

The elliptic curves in class 277200bb 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 \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 277200.2.a.bb

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 277200bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277200.bb4	277200bb1	\([0, 0, 0, -13275, -19365750]\)	\(-5545233/3469312\)	\(-161864220672000000\)	\([2]\)	\(2359296\)	\(1.9812\)	\(\Gamma_0(N)\)-optimal
277200.bb3	277200bb2	\([0, 0, 0, -1165275, -479013750]\)	\(3750606459153/45914176\)	\(2142171795456000000\)	\([2, 2]\)	\(4718592\)	\(2.3278\)
277200.bb2	277200bb3	\([0, 0, 0, -2173275, 473546250]\)	\(24331017010833/12004097336\)	\(560063165308416000000\)	\([2]\)	\(9437184\)	\(2.6743\)
277200.bb1	277200bb4	\([0, 0, 0, -18589275, -30849045750]\)	\(15226621995131793/2324168\)	\(108436382208000000\)	\([2]\)	\(9437184\)	\(2.6743\)