Cremona's table of elliptic curves

17856 = 2⁶ · 3² · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 31-	Signs for the Atkin-Lehner involutions
Class	17856bh	Isogeny class
Conductor	17856	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-22238862336 = -1 · 210 · 36 · 313	Discriminant
Eigenvalues	2+ 3- -3 -1 -6 -2 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,636,3656]	[a1,a2,a3,a4,a6]
Generators	[37:279:1]	Generators of the group modulo torsion
j	38112512/29791	j-invariant
L	2.8258315200179	L(r)(E,1)/r!
Ω	0.77474371020371	Real period
R	0.60790673586643	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	17856bw2 1116e2 1984f2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 17856bh2

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
+	-	-3	-1	-6	-2	-6	1	6	0	-	10	9	-8	0	0	-3	10	4	15	14	8	6	-12	-7

---

Quadratic twists for elliptic curve 17856bh2

-4	8	-3
17856bw2	1116e2	1984f2

---

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