Cremona's table of elliptic curves

570 = 2 · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	570a	Isogeny class
Conductor	570	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	5540400 = 24 · 36 · 52 · 19	Discriminant
Eigenvalues	2+ 3+ 5+  2 -6  0  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1618,24388]	[a1,a2,a3,a4,a6]
Generators	[16:46:1]	Generators of the group modulo torsion
j	468898230633769/5540400	j-invariant
L	1.3629838037782	L(r)(E,1)/r!
Ω	2.1867251700822	Real period
R	0.31164954389922	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	4560z2 18240bp2 1710r2 2850x2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570a2

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

---

Quadratic twists for elliptic curve 570a2

-4	8	-3	5	-7	-11	13	-19
4560z2	18240bp2	1710r2	2850x2	27930bz2	68970bq2	96330ct2	10830bc2

---

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