Elliptic curve isogeny class with LMFDB label 189225.g (Cremona label 189225k)

• Label: 189225.g
• Number of curves: $4$
• Conductor: $189225$
• CM: no
• Rank: $0$

Elliptic curves in class 189225.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
189225.g1	189225k3	$[1, -1, 1, -48729380, 129020370122]$	$1888690601881/31827645$	$215645324818954590703125$	$[2]$	$30965760$	$3.2753$
189225.g2	189225k2	$[1, -1, 1, -6153755, -2793764878]$	$3803721481/1703025$	$11538691577708628515625$	$[2, 2]$	$15482880$	$2.9287$
189225.g3	189225k1	$[1, -1, 1, -5207630, -4570587628]$	$2305199161/1305$	$8841909254949140625$	$[2]$	$7741440$	$2.5822$	$\Gamma_0(N)$-optimal
189225.g4	189225k4	$[1, -1, 1, 21283870, -20902597378]$	$157376536199/118918125$	$-805718980857240439453125$	$[2]$	$30965760$	$3.2753$

Rank

The elliptic curves in class 189225.g have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1$
$5$	$1$
$29$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + T + 2 T^{2}$	1.2.b
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 6 T + 13 T^{2}$	1.13.g
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 189225.g do not have complex multiplication.

Modular form 189225.2.a.g

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.