Cremona's table of elliptic curves

20 = 2² · 5

Field	Data	Notes
Atkin-Lehner	2- 5+	Signs for the Atkin-Lehner involutions
Class	20a	Isogeny class
Conductor	20	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	80 = 24 · 5	Discriminant
Eigenvalues	2- -2 5+  2  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1,0]	[a1,a2,a3,a4,a6]
j	16384/5	j-invariant
L	0.47072919032652	L(r)(E,1)/r!
Ω	5.6487502839182	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	80b2 320c1 180a1 100a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20a2

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

---

Quadratic twists for elliptic curve 20a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79
80b2	320c1	180a1	100a1	980g1	2420e1	3380i1	5780e1	7220c1	10580m1	16820b1	19220b1	27380d1	33620a1	36980a1	44180g1	56180d1	69620b1	74420d1	89780f1	100820a1	106580d1	124820b1

---

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