Elliptic curve isogeny class with LMFDB label 278850.gy (Cremona label 278850gy)

• Label: 278850.gy
• Number of curves: $4$
• Conductor: $278850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 278850.gy have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 278850.gy do not have complex multiplication.

Modular form 278850.2.a.gy

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 278850.gy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
278850.gy1	278850gy3	\([1, 0, 0, -25797938, 50432004492]\)	\(25176685646263969/57915000\)	\(4367885050546875000\)	\([2]\)	\(18579456\)	\(2.8202\)
278850.gy2	278850gy2	\([1, 0, 0, -1630938, 768819492]\)	\(6361447449889/294465600\)	\(22208268879225000000\)	\([2, 2]\)	\(9289728\)	\(2.4736\)
278850.gy3	278850gy1	\([1, 0, 0, -278938, -41028508]\)	\(31824875809/8785920\)	\(662624339520000000\)	\([2]\)	\(4644864\)	\(2.1271\)	\(\Gamma_0(N)\)-optimal
278850.gy4	278850gy4	\([1, 0, 0, 904062, 2941314492]\)	\(1083523132511/50179392120\)	\(-3784474085927266875000\)	\([2]\)	\(18579456\)	\(2.8202\)