Elliptic curve isogeny class with LMFDB label 9248.f (Cremona label 9248e)

• Label: 9248.f
• Number of curves: $4$
• Conductor: $9248$
• CM: $\Q(\sqrt{-1})$
• Rank: $0$

Elliptic curves in class 9248.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
9248.f1	9248e2	$[0, 0, 0, -3179, -68782]$	$287496$	$12358435328$	$[2]$	$5120$	$0.79922$		$-16$
9248.f2	9248e3	$[0, 0, 0, -3179, 68782]$	$287496$	$12358435328$	$[2]$	$5120$	$0.79922$		$-16$
9248.f3	9248e1	$[0, 0, 0, -289, 0]$	$1728$	$1544804416$	$[2, 2]$	$2560$	$0.45265$	$\Gamma_0(N)$-optimal	$-4$
9248.f4	9248e4	$[0, 0, 0, 1156, 0]$	$1728$	$-98867482624$	$[2]$	$5120$	$0.79922$		$-4$

Rank

The elliptic curves in class 9248.f have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$17$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T^{2}$	1.3.a
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 - 10 T + 29 T^{2}$	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 9248.f has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-1})$.

Modular form 9248.2.a.f

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.