Elliptic curve isogeny class with LMFDB label 3360.i (Cremona label 3360p)

• Label: 3360.i
• Number of curves: $4$
• Conductor: $3360$
• CM: no
• Rank: $0$

Elliptic curves in class 3360.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3360.i1	3360p2	$[0, -1, 0, -1120, -14060]$	$303735479048/105$	$53760$	$[2]$	$1536$	$0.26359$
3360.i2	3360p3	$[0, -1, 0, -145, 385]$	$82881856/36015$	$147517440$	$[4]$	$1536$	$0.26359$
3360.i3	3360p1	$[0, -1, 0, -70, -200]$	$601211584/11025$	$705600$	$[2, 2]$	$768$	$-0.082988$	$\Gamma_0(N)$-optimal
3360.i4	3360p4	$[0, -1, 0, 0, -648]$	$-8/354375$	$-181440000$	$[2]$	$1536$	$0.26359$

Rank

The elliptic curves in class 3360.i have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$5$	$1 - T$
$7$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 8 T + 23 T^{2}$	1.23.ai
$29$	$1 - 10 T + 29 T^{2}$	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3360.i do not have complex multiplication.

Modular form 3360.2.a.i

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.