Elliptic curve isogeny class with Cremona label 155584bf (LMFDB label 155584.bc)

• Label: 155584bf
• Number of curves: $2$
• Conductor: $155584$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 155584bf have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 155584bf do not have complex multiplication.

Modular form 155584.2.a.bf

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 155584bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
155584.bc1	155584bf1	\([0, -1, 0, -2465, -43999]\)	\(6321363049/347633\)	\(91129905152\)	\([2]\)	\(229376\)	\(0.85851\)	\(\Gamma_0(N)\)-optimal
155584.bc2	155584bf2	\([0, -1, 0, 1695, -181279]\)	\(2053225511/55006237\)	\(-14419554992128\)	\([2]\)	\(458752\)	\(1.2051\)