Cremona's table of elliptic curves

3822 = 2 · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	3822f	Isogeny class
Conductor	3822	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-4310828744441856 = -1 · 227 · 3 · 77 · 13	Discriminant
Eigenvalues	2+ 3+ -3 7-  3 13+  3  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1276769,554763189]	[a1,a2,a3,a4,a6]
j	-1956469094246217097/36641439744	j-invariant
L	0.80440754567736	L(r)(E,1)/r!
Ω	0.40220377283868	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	30576cr3 122304ek3 11466cc3 95550jz3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822f3

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	-	3	+	3	7	9	-9	4	-7	-12	-1	0	-6	-12	1	14	12	7	-10	6	6	10

---

Quadratic twists for elliptic curve 3822f3

-4	8	-3	5	-7	13
30576cr3	122304ek3	11466cc3	95550jz3	546d3	49686cj3

---

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