Elliptic curve isogeny class with LMFDB label 15.a (Cremona label 15a)

• Label: 15.a
• Number of curves: $8$
• Conductor: $15$
• CM: no
• Rank: $0$

Elliptic curves in class 15.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15.a1	15a5	$[1, 1, 1, -2160, -39540]$	$1114544804970241/405$	$405$	$[2]$	$4$	$0.29087$
15.a2	15a2	$[1, 1, 1, -135, -660]$	$272223782641/164025$	$164025$	$[2, 2]$	$2$	$-0.055704$
15.a3	15a6	$[1, 1, 1, -110, -880]$	$-147281603041/215233605$	$-215233605$	$[2]$	$4$	$0.29087$
15.a4	15a7	$[1, 1, 1, -80, 242]$	$56667352321/15$	$15$	$[4]$	$4$	$-0.40228$
15.a5	15a1	$[1, 1, 1, -10, -10]$	$111284641/50625$	$50625$	$[2, 4]$	$1$	$-0.40228$	$\Gamma_0(N)$-optimal
15.a6	15a3	$[1, 1, 1, -5, 2]$	$13997521/225$	$225$	$[2, 4]$	$2$	$-0.74885$
15.a7	15a8	$[1, 1, 1, 0, 0]$	$-1/15$	$-15$	$[4]$	$4$	$-1.0954$
15.a8	15a4	$[1, 1, 1, 35, -28]$	$4733169839/3515625$	$-3515625$	$[8]$	$2$	$-0.055704$

Rank

The elliptic curves in class 15.a have rank $0$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + T + 2 T^{2}$	1.2.b
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 15.a do not have complex multiplication.

Modular form 15.2.a.a

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.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.