Cremona's table of elliptic curves

8272 = 2⁴ · 11 · 47

Field	Data	Notes
Atkin-Lehner	2- 11+ 47-	Signs for the Atkin-Lehner involutions
Class	8272j	Isogeny class
Conductor	8272	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-292365568 = -1 · 28 · 11 · 473	Discriminant
Eigenvalues	2-  2  0  1 11+  5 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2188,40140]	[a1,a2,a3,a4,a6]
Generators	[234:141:8]	Generators of the group modulo torsion
j	-4527142594000/1142053	j-invariant
L	6.1333107035201	L(r)(E,1)/r!
Ω	1.6878241120086	Real period
R	1.2112855164395	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2068d2 33088bk2 74448bj2 90992bc2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8272j2

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
-	2	0	1	+	5	-6	4	-9	-6	-5	-1	9	-8	-	-9	12	2	7	-6	-10	-5	-3	-15	-7

---

Quadratic twists for elliptic curve 8272j2

-4	8	-3	-11
2068d2	33088bk2	74448bj2	90992bc2

---

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