Elliptic curve isogeny class with LMFDB label 230640.db (Cremona label 230640db)

• Label: 230640.db
• Number of curves: $4$
• Conductor: $230640$
• CM: no
• Rank: $0$

Elliptic curves in class 230640.db

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
230640.db1	230640db3	$[0, 1, 0, -6381360, 6202188468]$	$15811147933922/1016955$	$1848425074506455040$	$[4]$	$5898240$	$2.5626$
230640.db2	230640db4	$[0, 1, 0, -2152960, -1142465452]$	$607199886722/41558445$	$75536942928150620160$	$[2]$	$5898240$	$2.5626$
230640.db3	230640db2	$[0, 1, 0, -423160, 84308708]$	$9220796644/1946025$	$1768554855237657600$	$[2, 2]$	$2949120$	$2.2160$
230640.db4	230640db1	$[0, 1, 0, 57340, 8005308]$	$91765424/174375$	$-39618164319840000$	$[2]$	$1474560$	$1.8695$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 230640.db have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$5$	$1 - T$
$31$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 230640.db do not have complex multiplication.

Modular form 230640.2.a.db

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.