Elliptic curve isogeny class with Cremona label 5491a (LMFDB label 5491.b)

• Label: 5491a
• Number of curves: $3$
• Conductor: $5491$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5491a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(17\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5491a do not have complex multiplication.

Modular form 5491.2.a.a

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 5491a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5491.b3	5491a1	\([0, -1, 1, 193, -110]\)	\(32768/19\)	\(-458613811\)	\([]\)	\(1680\)	\(0.35143\)	\(\Gamma_0(N)\)-optimal
5491.b2	5491a2	\([0, -1, 1, -2697, -56465]\)	\(-89915392/6859\)	\(-165559585771\)	\([]\)	\(5040\)	\(0.90074\)
5491.b1	5491a3	\([0, -1, 1, -222337, -40278040]\)	\(-50357871050752/19\)	\(-458613811\)	\([]\)	\(15120\)	\(1.4500\)