Elliptic curve isogeny class with LMFDB label 152880.f (Cremona label 152880ec)

• Label: 152880.f
• Number of curves: $6$
• Conductor: $152880$
• CM: no
• Rank: $1$

Elliptic curves in class 152880.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
152880.f1	152880ec6	$[0, -1, 0, -107153216, -426866360640]$	$282352188585428161201/20813369346315$	$10029760881560016629760$	$[2]$	$18874368$	$3.2720$
152880.f2	152880ec3	$[0, -1, 0, -36730416, 85693380480]$	$11372424889583066401/50586128775$	$24376964973567897600$	$[2]$	$9437184$	$2.9254$
152880.f3	152880ec4	$[0, -1, 0, -7134416, -5747205120]$	$83339496416030401/18593645841225$	$8960097646896250982400$	$[2, 2]$	$9437184$	$2.9254$
152880.f4	152880ec2	$[0, -1, 0, -2332416, 1294447680]$	$2912015927948401/184878500625$	$89091156869245440000$	$[2, 2]$	$4718592$	$2.5788$
152880.f5	152880ec1	$[0, -1, 0, 117584, 85127680]$	$373092501599/6718359375$	$-3237512241600000000$	$[2]$	$2359296$	$2.2322$	$\Gamma_0(N)$-optimal
152880.f6	152880ec5	$[0, -1, 0, 16052384, -35370660800]$	$949279533867428399/1670570708285115$	$-805031826469009386024960$	$[2]$	$18874368$	$3.2720$

Rank

The elliptic curves in class 152880.f have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$5$	$1 + T$
$7$	$1$
$13$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 23 T^{2}$	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 152880.f do not have complex multiplication.

Modular form 152880.2.a.f

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.