Elliptic curve isogeny class with Cremona label 20a (LMFDB label 20.a)

• Label: 20a
• Number of curves: $4$
• Conductor: $20$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 20a have rank $0$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$11$	$1 + 11 T^{2}$	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
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20a do not have complex multiplication.

Modular form 20.2.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 Cremona 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 Cremona labels.

Elliptic curves in class 20a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20.a4	20a1	$[0, 1, 0, 4, 4]$	$21296/25$	$-6400$	$[6]$	$1$	$-0.58338$	$\Gamma_0(N)$-optimal
20.a3	20a2	$[0, 1, 0, -1, 0]$	$16384/5$	$80$	$[6]$	$2$	$-0.92995$
20.a2	20a3	$[0, 1, 0, -36, -140]$	$-20720464/15625$	$-4000000$	$[2]$	$3$	$-0.034070$
20.a1	20a4	$[0, 1, 0, -41, -116]$	$488095744/125$	$2000$	$[2]$	$6$	$-0.38064$