Cremona's table of elliptic curves

522 = 2 · 3² · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 29-	Signs for the Atkin-Lehner involutions
Class	522c	Isogeny class
Conductor	522	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-4566456 = -1 · 23 · 39 · 29	Discriminant
Eigenvalues	2+ 3+ -3 -1  0  2  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1311,-17947]	[a1,a2,a3,a4,a6]
j	-12665630691/232	j-invariant
L	0.79338297587091	L(r)(E,1)/r!
Ω	0.39669148793545	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4176u2 16704e2 522h1 13050bb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 522c2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	-3	-1	0	2	3	5	6	-	-4	11	3	-1	3	-6	9	2	8	6	8	-16	12	6	-4

---

Quadratic twists for elliptic curve 522c2

-4	8	-3	5	-7	-11	13	29
4176u2	16704e2	522h1	13050bb2	25578g2	63162bo2	88218br2	15138s2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations