Elliptic curve isogeny class with Cremona label 57330c (LMFDB label 57330.o)

• Label: 57330c
• Number of curves: $4$
• Conductor: $57330$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 57330c have rank \(0\).

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
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 57330.2.a.c

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 57330c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57330.o3	57330c1	\([1, -1, 0, -12210, -521984]\)	\(-63378025803/812500\)	\(-2580924937500\)	\([2]\)	\(165888\)	\(1.1909\)	\(\Gamma_0(N)\)-optimal
57330.o2	57330c2	\([1, -1, 0, -195960, -33339734]\)	\(261984288445803/42250\)	\(134208096750\)	\([2]\)	\(331776\)	\(1.5375\)
57330.o4	57330c3	\([1, -1, 0, 42915, -2681659]\)	\(3774555693/3515200\)	\(-8140096850558400\)	\([2]\)	\(497664\)	\(1.7402\)
57330.o1	57330c4	\([1, -1, 0, -221685, -24008419]\)	\(520300455507/193072360\)	\(447094819516920120\)	\([2]\)	\(995328\)	\(2.0868\)