Elliptic curve isogeny class with LMFDB label 393129.bl (Cremona label 393129bl)

• Label: 393129.bl
• Number of curves: $2$
• Conductor: $393129$
• CM: $\Q(\sqrt{-19})$
• Rank: $1$

Elliptic curves in class 393129.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
393129.bl1	393129bl2	$[0, 0, 1, -14938902, -22245892441]$	$-884736$	$-416740825671930940851$	$[]$	$14470400$	$2.8703$		$-19$
393129.bl2	393129bl1	$[0, 0, 1, -41382, 3243314]$	$-884736$	$-8858178799371$	$[]$	$761600$	$1.3981$	$\Gamma_0(N)$-optimal	$-19$

Rank

The elliptic curves in class 393129.bl have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1$
$11$	$1$
$19$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + 2 T^{2}$	1.2.a
$5$	$1 - T + 5 T^{2}$	1.5.ab
$7$	$1 + 3 T + 7 T^{2}$	1.7.d
$13$	$1 + 13 T^{2}$	1.13.a
$17$	$1 + 7 T + 17 T^{2}$	1.17.h
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 393129.bl has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-19})$.

Modular form 393129.2.a.bl

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.

$\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.