Cremona's table of elliptic curves

3588 = 2² · 3 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 23+	Signs for the Atkin-Lehner involutions
Class	3588d	Isogeny class
Conductor	3588	Conductor
∏ cp	60	Product of Tamagawa factors cp
Δ	4536651661238631168 = 28 · 35 · 1310 · 232	Discriminant
Eigenvalues	2- 3+  0  2  0 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-809348,-260576184]	[a1,a2,a3,a4,a6]
Generators	[-458:3718:1]	Generators of the group modulo torsion
j	229028841865443058000/17721295551713403	j-invariant
L	3.1916452296722	L(r)(E,1)/r!
Ω	0.15995162099173	Real period
R	1.3302544064609	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	14352bh2 57408x2 10764k2 89700r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3588d2

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

---

Quadratic twists for elliptic curve 3588d2

-4	8	-3	5	13	-23
14352bh2	57408x2	10764k2	89700r2	46644b2	82524d2

---

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