Elliptic curve isogeny class with Cremona label 59584bn (LMFDB label 59584.u)

• Label: 59584bn
• Number of curves: $3$
• Conductor: $59584$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 59584bn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 59584bn do not have complex multiplication.

Modular form 59584.2.a.bn

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 59584bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
59584.u3	59584bn1	\([0, 1, 0, 131, 69]\)	\(32768/19\)	\(-143061184\)	\([]\)	\(18144\)	\(0.25436\)	\(\Gamma_0(N)\)-optimal
59584.u2	59584bn2	\([0, 1, 0, -1829, 31429]\)	\(-89915392/6859\)	\(-51645087424\)	\([]\)	\(54432\)	\(0.80366\)
59584.u1	59584bn3	\([0, 1, 0, -150789, 22487149]\)	\(-50357871050752/19\)	\(-143061184\)	\([]\)	\(163296\)	\(1.3530\)