Cremona's table of elliptic curves

21675 = 3 · 5² · 17²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	21675f	Isogeny class
Conductor	21675	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	165888	Modular degree for the optimal curve
Δ	-1360795882803075 = -1 · 33 · 52 · 1710	Discriminant
Eigenvalues	2 3+ 5+  1 -2  7 17+  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-31308,-2763817]	[a1,a2,a3,a4,a6]
Generators	[333581392607152382:-9109874397693471037:421841250899992]	Generators of the group modulo torsion
j	-5624320000/2255067	j-invariant
L	9.2977007231462	L(r)(E,1)/r!
Ω	0.17597654512199	Real period
R	26.417443065214	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	65025bu1 21675ba1 1275f1	Quadratic twists by: -3 5 17

Hecke Eigenvalues for elliptic curve 21675f1

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	+	+	1	-2	7	+	3	-6	-6	7	2	-4	-1	-6	-8	-10	5	-5	-4	-14	8	14	-12	5

---

Quadratic twists for elliptic curve 21675f1

-3	5	17
65025bu1	21675ba1	1275f1

---

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