Elliptic curve isogeny class with LMFDB label 122304.dk (Cremona label 122304ga)

• Label: 122304.dk
• Number of curves: $4$
• Conductor: $122304$
• CM: no
• Rank: $0$

Elliptic curves in class 122304.dk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122304.dk1	122304ga4	$[0, -1, 0, -163137, -25307295]$	$62275269892/39$	$300699549696$	$[2]$	$393216$	$1.5227$
122304.dk2	122304ga2	$[0, -1, 0, -10257, -387855]$	$61918288/1521$	$2931820609536$	$[2, 2]$	$196608$	$1.1761$
122304.dk3	122304ga1	$[0, -1, 0, -1437, 12573]$	$2725888/1053$	$126857622528$	$[2]$	$98304$	$0.82951$	$\Gamma_0(N)$-optimal
122304.dk4	122304ga3	$[0, -1, 0, 1503, -1236927]$	$48668/85683$	$-660636910682112$	$[2]$	$393216$	$1.5227$

Rank

The elliptic curves in class 122304.dk have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$7$	$1$
$13$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$11$	$1 + 11 T^{2}$	1.11.a
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 - 4 T + 19 T^{2}$	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 122304.dk do not have complex multiplication.

Modular form 122304.2.a.dk

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.