Elliptic curve isogeny class with LMFDB label 1980.f (Cremona label 1980d)

• Label: 1980.f
• Number of curves: $4$
• Conductor: $1980$
• CM: no
• Rank: $0$

Elliptic curves in class 1980.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1980.f1	1980d4	$[0, 0, 0, -2249967, 1299009526]$	$6749703004355978704/5671875$	$1058508000000$	$[6]$	$13824$	$2.0429$
1980.f2	1980d3	$[0, 0, 0, -140592, 20306401]$	$-26348629355659264/24169921875$	$-281917968750000$	$[6]$	$6912$	$1.6963$
1980.f3	1980d2	$[0, 0, 0, -28407, 1696894]$	$13584145739344/1195803675$	$223165665043200$	$[2]$	$4608$	$1.4936$
1980.f4	1980d1	$[0, 0, 0, 1968, 123469]$	$72268906496/606436875$	$-7073479710000$	$[2]$	$2304$	$1.1470$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1980.f have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1 - T$
$11$	$1 + T$

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 1980.f do not have complex multiplication.

Modular form 1980.2.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.

$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.