Elliptic curve isogeny class with Cremona label 520a (LMFDB label 520.a)

• Label: 520a
• Number of curves: $4$
• Conductor: $520$
• CM: no
• Rank: $1$

Elliptic curves in class 520a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
520.a3	520a1	$[0, 0, 0, -23, 42]$	$5256144/65$	$16640$	$[2]$	$32$	$-0.38003$	$\Gamma_0(N)$-optimal
520.a2	520a2	$[0, 0, 0, -43, -42]$	$8586756/4225$	$4326400$	$[2, 2]$	$64$	$-0.033453$
520.a1	520a3	$[0, 0, 0, -563, -5138]$	$9636491538/8125$	$16640000$	$[2]$	$128$	$0.31312$
520.a4	520a4	$[0, 0, 0, 157, -322]$	$208974222/142805$	$-292464640$	$[2]$	$128$	$0.31312$

Rank

The elliptic curves in class 520a have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T^{2}$	1.3.a
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 - 4 T + 19 T^{2}$	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 520a do not have complex multiplication.

Modular form 520.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.