Elliptic curve isogeny class with Cremona label 180336bz (LMFDB label 180336.bz)

• Label: 180336bz
• Number of curves: $4$
• Conductor: $180336$
• CM: no
• Rank: $1$

Elliptic curves in class 180336bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
180336.bz3	180336bz1	$[0, 1, 0, -2119, -22360]$	$2725888/1053$	$406669762512$	$[2]$	$163840$	$0.92659$	$\Gamma_0(N)$-optimal
180336.bz2	180336bz2	$[0, 1, 0, -15124, 695516]$	$61918288/1521$	$9398590066944$	$[2, 2]$	$327680$	$1.2732$
180336.bz1	180336bz3	$[0, 1, 0, -240544, 45328676]$	$62275269892/39$	$963957955584$	$[2]$	$655360$	$1.6197$
180336.bz4	180336bz4	$[0, 1, 0, 2216, 2214500]$	$48668/85683$	$-2117815628418048$	$[2]$	$655360$	$1.6197$

Rank

The elliptic curves in class 180336bz have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$13$	$1 - T$
$17$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 11 T^{2}$	1.11.a
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 180336bz do not have complex multiplication.

Modular form 180336.2.a.bz

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.

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.