Elliptic curve isogeny class with LMFDB label 585.h (Cremona label 585h)

• Label: 585.h
• Number of curves: $2$
• Conductor: $585$
• CM: no
• Rank: $1$

Elliptic curves in class 585.h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
585.h1	585h1	$[1, -1, 0, -9, 0]$	$117649/65$	$47385$	$[2]$	$48$	$-0.41231$	$\Gamma_0(N)$-optimal
585.h2	585h2	$[1, -1, 0, 36, -27]$	$6967871/4225$	$-3080025$	$[2]$	$96$	$-0.065735$

Rank

The elliptic curves in class 585.h have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1$
$5$	$1 - T$
$13$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - T + 2 T^{2}$	1.2.ab
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 6 T + 19 T^{2}$	1.19.g
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 585.h do not have complex multiplication.

Modular form 585.2.a.h

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.