Elliptic curve isogeny class with LMFDB label 1584.g (Cremona label 1584p)

• Label: 1584.g
• Number of curves: $3$
• Conductor: $1584$
• CM: no
• Rank: $0$

Elliptic curves in class 1584.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1584.g1	1584p3	$[0, 0, 0, -1126128, -459970256]$	$-52893159101157376/11$	$-32845824$	$[]$	$6000$	$1.7392$
1584.g2	1584p2	$[0, 0, 0, -1488, -40016]$	$-122023936/161051$	$-480895709184$	$[]$	$1200$	$0.93444$
1584.g3	1584p1	$[0, 0, 0, -48, 304]$	$-4096/11$	$-32845824$	$[]$	$240$	$0.12972$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1584.g have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$11$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + T + 5 T^{2}$	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
$23$	$1 + T + 23 T^{2}$	1.23.b
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1584.g do not have complex multiplication.

Modular form 1584.2.a.g

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.