Cremona's table of elliptic curves

8200 = 2³ · 5² · 41

Field	Data	Notes
Atkin-Lehner	2+ 5+ 41-	Signs for the Atkin-Lehner involutions
Class	8200c	Isogeny class
Conductor	8200	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	6560000000 = 211 · 57 · 41	Discriminant
Eigenvalues	2+  0 5+  0  4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-218675,-39359250]	[a1,a2,a3,a4,a6]
j	36138584631042/205	j-invariant
L	1.7661995021753	L(r)(E,1)/r!
Ω	0.22077493777191	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16400g3 65600n4 73800bz4 1640g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8200c3

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
+	0	+	0	4	-6	2	4	8	-6	8	-6	-	-4	0	-6	12	6	-8	4	6	4	-12	-14	10

---

Quadratic twists for elliptic curve 8200c3

-4	8	-3	5
16400g3	65600n4	73800bz4	1640g3

---

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