Elliptic curve isogeny class with LMFDB label 384.d (Cremona label 384f)

• Label: 384.d
• Number of curves: $2$
• Conductor: $384$
• CM: no
• Rank: $0$

Elliptic curves in class 384.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
384.d1	384f2	$[0, -1, 0, -141, 693]$	$19056256/27$	$442368$	$[2]$	$96$	$-0.013528$
384.d2	384f1	$[0, -1, 0, -6, 18]$	$-219488/729$	$-93312$	$[2]$	$48$	$-0.36010$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 384.d have rank $0$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 4 T + 5 T^{2}$	1.5.ae
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 - 8 T + 19 T^{2}$	1.19.ai
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 384.d do not have complex multiplication.

Modular form 384.2.a.d

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.