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

• Label: 277440.es
• Number of curves: $4$
• Conductor: $277440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 277440.es have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 19 T^{2}\)	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 277440.es do not have complex multiplication.

Modular form 277440.2.a.es

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 277440.es

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277440.es1	277440es3	\([0, -1, 0, -555265, 159441985]\)	\(23937672968/45\)	\(35592293744640\)	\([2]\)	\(2359296\)	\(1.8555\)
277440.es2	277440es4	\([0, -1, 0, -92865, -7623135]\)	\(111980168/32805\)	\(25946782139842560\)	\([2]\)	\(2359296\)	\(1.8555\)
277440.es3	277440es2	\([0, -1, 0, -35065, 2445625]\)	\(48228544/2025\)	\(200206652313600\)	\([2, 2]\)	\(1179648\)	\(1.5089\)
277440.es4	277440es1	\([0, -1, 0, 1060, 140850]\)	\(85184/5625\)	\(-8689524840000\)	\([2]\)	\(589824\)	\(1.1624\)	\(\Gamma_0(N)\)-optimal