Elliptic curve isogeny class with Cremona label 5819a (LMFDB label 5819.a)

• Label: 5819a
• Number of curves: $3$
• Conductor: $5819$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5819a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(11\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5819a do not have complex multiplication.

Modular form 5819.2.a.a

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 5819a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5819.a3	5819a1	\([0, -1, 1, -176, -2082]\)	\(-4096/11\)	\(-1628394779\)	\([]\)	\(2530\)	\(0.45502\)	\(\Gamma_0(N)\)-optimal
5819.a2	5819a2	\([0, -1, 1, -5466, 283578]\)	\(-122023936/161051\)	\(-23841327959339\)	\([]\)	\(12650\)	\(1.2597\)
5819.a1	5819a3	\([0, -1, 1, -4136956, 3240070018]\)	\(-52893159101157376/11\)	\(-1628394779\)	\([]\)	\(63250\)	\(2.0645\)