Elliptic curve isogeny class with LMFDB label 258720.bj (Cremona label 258720bj)

• Label: 258720.bj
• Number of curves: $4$
• Conductor: $258720$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 258720.bj have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 258720.bj do not have complex multiplication.

Modular form 258720.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 258720.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
258720.bj1	258720bj2	\([0, -1, 0, -4272081, 3400074945]\)	\(17893449053367616/39220335\)	\(18899899156131840\)	\([2]\)	\(5898240\)	\(2.3694\)
258720.bj2	258720bj4	\([0, -1, 0, -733056, -173288520]\)	\(723231880398728/202569142545\)	\(12202013210253672960\)	\([2]\)	\(5898240\)	\(2.3694\)
258720.bj3	258720bj1	\([0, -1, 0, -270006, 51939000]\)	\(289119478354624/13074779025\)	\(98447019360782400\)	\([2, 2]\)	\(2949120\)	\(2.0229\)	\(\Gamma_0(N)\)-optimal
258720.bj4	258720bj3	\([0, -1, 0, 145024, 196867476]\)	\(5599924283512/281331579375\)	\(-16946370038727360000\)	\([2]\)	\(5898240\)	\(2.3694\)