Elliptic curve isogeny class with Cremona label 130130bq (LMFDB label 130130.bq)

• Label: 130130bq
• Number of curves: $4$
• Conductor: $130130$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 130130bq have rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 130130bq do not have complex multiplication.

Modular form 130130.2.a.bq

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 130130bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
130130.bq3	130130bq1	\([1, 0, 0, -154385, 23434345]\)	\(-84309998289049/414124480\)	\(-1998899767184320\)	\([2]\)	\(1327104\)	\(1.7841\)	\(\Gamma_0(N)\)-optimal
130130.bq2	130130bq2	\([1, 0, 0, -2473065, 1496723617]\)	\(346553430870203929/8300600\)	\(40065410785400\)	\([2]\)	\(2654208\)	\(2.1307\)
130130.bq4	130130bq3	\([1, 0, 0, 383880, 124520512]\)	\(1296134247276791/2137096192000\)	\(-10315355133411328000\)	\([2]\)	\(3981312\)	\(2.3334\)
130130.bq1	130130bq4	\([1, 0, 0, -2644600, 1277160000]\)	\(423783056881319689/99207416000000\)	\(478855248415544000000\)	\([2]\)	\(7962624\)	\(2.6800\)