Elliptic curve isogeny class with LMFDB label 57330.en (Cremona label 57330ev)

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

Rank

The elliptic curves in class 57330.en 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 57330.2.a.en

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 57330.en

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57330.en1	57330ev4	\([1, -1, 1, -384806687, -2905324886649]\)	\(73474353581350183614361/576510977802240\)	\(49445110280015229911040\)	\([2]\)	\(12441600\)	\(3.5276\)
57330.en2	57330ev3	\([1, -1, 1, -23539487, -47412320889]\)	\(-16818951115904497561/1592332281446400\)	\(-136568163122737997414400\)	\([2]\)	\(6220800\)	\(3.1811\)
57330.en3	57330ev2	\([1, -1, 1, -7057112, 273406011]\)	\(453198971846635561/261896250564000\)	\(22461825515318342244000\)	\([2]\)	\(4147200\)	\(2.9783\)
57330.en4	57330ev1	\([1, -1, 1, 1762888, 33502011]\)	\(7064514799444439/4094064000000\)	\(-351131988405744000000\)	\([2]\)	\(2073600\)	\(2.6318\)	\(\Gamma_0(N)\)-optimal