Cremona's table of elliptic curves

528 = 2⁴ · 3 · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	528g	Isogeny class
Conductor	528	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-722608128 = -1 · 213 · 36 · 112	Discriminant
Eigenvalues	2- 3+  0 -2 11- -4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,72,-1296]	[a1,a2,a3,a4,a6]
Generators	[20:88:1]	Generators of the group modulo torsion
j	9938375/176418	j-invariant
L	1.7226781593617	L(r)(E,1)/r!
Ω	0.78176008867867	Real period
R	0.55089732269186	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	66a2 2112x2 1584l2 13200ck2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528g2

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

---

Quadratic twists for elliptic curve 528g2

-4	8	-3	5	-7	-11	13
66a2	2112x2	1584l2	13200ck2	25872cw2	5808p2	89232y2

---

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