Elliptic curve isogeny class with LMFDB label 57330.dh (Cremona label 57330em)

• Label: 57330.dh
• Number of curves: $4$
• Conductor: $57330$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 57330.dh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 57330.dh do not have complex multiplication.

Modular form 57330.2.a.dh

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 57330.dh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57330.dh1	57330em4	\([1, -1, 1, -39515153, -95597983519]\)	\(79560762543506753209/479824800\)	\(41152711855600800\)	\([2]\)	\(3932160\)	\(2.7961\)
57330.dh2	57330em2	\([1, -1, 1, -2471153, -1491405919]\)	\(19458380202497209/47698560000\)	\(4090920468485760000\)	\([2, 2]\)	\(1966080\)	\(2.4495\)
57330.dh3	57330em3	\([1, -1, 1, -1553873, -2613055903]\)	\(-4837870546133689/31603162500000\)	\(-2710480658957662500000\)	\([2]\)	\(3932160\)	\(2.7961\)
57330.dh4	57330em1	\([1, -1, 1, -213233, -3888223]\)	\(12501706118329/7156531200\)	\(613787920839475200\)	\([4]\)	\(983040\)	\(2.1029\)	\(\Gamma_0(N)\)-optimal