Elliptic curve isogeny class with Cremona label 60990bj (LMFDB label 60990.bh)

• Label: 60990bj
• Number of curves: $3$
• Conductor: $60990$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 60990bj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(19\)	\(1 + T\)
\(107\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 60990bj do not have complex multiplication.

Modular form 60990.2.a.bj

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 60990bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
60990.bh2	60990bj1	\([1, 0, 0, -231240, 187785792]\)	\(-1367453954870275397761/14445609579000000000\)	\(-14445609579000000000\)	\([9]\)	\(1469664\)	\(2.3585\)	\(\Gamma_0(N)\)-optimal
60990.bh3	60990bj2	\([1, 0, 0, 2063760, -4837643208]\)	\(972078350597918586282239/10673270244457546419000\)	\(-10673270244457546419000\)	\([3]\)	\(4408992\)	\(2.9078\)
60990.bh1	60990bj3	\([1, 0, 0, -165638790, -821071057998]\)	\(-502585390635922447924416132961/378299752139695192905390\)	\(-378299752139695192905390\)	\([]\)	\(13226976\)	\(3.4571\)