Elliptic curve isogeny class with Cremona label 330330fj (LMFDB label 330330.fj)

• Label: 330330fj
• Number of curves: $4$
• Conductor: $330330$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 330330fj have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 330330fj do not have complex multiplication.

Modular form 330330.2.a.fj

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 330330fj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
330330.fj3	330330fj1	\([1, 0, 0, -91781, 4797981]\)	\(48264326765929/22299191460\)	\(39504377922069060\)	\([2]\)	\(3732480\)	\(1.8793\)	\(\Gamma_0(N)\)-optimal
330330.fj4	330330fj2	\([1, 0, 0, 323249, 36257255]\)	\(2108526614950391/1540302022350\)	\(-2728738991016388350\)	\([2]\)	\(7464960\)	\(2.2258\)
330330.fj1	330330fj3	\([1, 0, 0, -6228296, 5982243840]\)	\(15082569606665230489/7751016000\)	\(13731397655976000\)	\([2]\)	\(11197440\)	\(2.4286\)
330330.fj2	330330fj4	\([1, 0, 0, -6194416, 6050552696]\)	\(-14837772556740428569/342100087875000\)	\(-606051173775922875000\)	\([2]\)	\(22394880\)	\(2.7752\)