Elliptic curve isogeny class with Cremona label 109330ba (LMFDB label 109330.ba)

• Label: 109330ba
• Number of curves: $4$
• Conductor: $109330$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 109330ba have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(29\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 109330ba do not have complex multiplication.

Modular form 109330.2.a.ba

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 109330ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
109330.ba2	109330ba1	\([1, 1, 1, -27350, 1719235]\)	\(3803721481/26000\)	\(15465406346000\)	\([2]\)	\(580608\)	\(1.3648\)	\(\Gamma_0(N)\)-optimal
109330.ba3	109330ba2	\([1, 1, 1, -10530, 3831827]\)	\(-217081801/10562500\)	\(-6282821328062500\)	\([2]\)	\(1161216\)	\(1.7114\)
109330.ba1	109330ba3	\([1, 1, 1, -174525, -27009325]\)	\(988345570681/44994560\)	\(26763813606133760\)	\([2]\)	\(1741824\)	\(1.9141\)
109330.ba4	109330ba4	\([1, 1, 1, 94595, -102470573]\)	\(157376536199/7722894400\)	\(-4593757694740302400\)	\([2]\)	\(3483648\)	\(2.2607\)