Cremona's table of elliptic curves

27600 = 2⁴ · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 23+	Signs for the Atkin-Lehner involutions
Class	27600c	Isogeny class
Conductor	27600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	-268272000000 = -1 · 210 · 36 · 56 · 23	Discriminant
Eigenvalues	2+ 3+ 5+  2  2  2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1608,35712]	[a1,a2,a3,a4,a6]
Generators	[6:162:1]	Generators of the group modulo torsion
j	-28756228/16767	j-invariant
L	5.4394861228273	L(r)(E,1)/r!
Ω	0.90849979825178	Real period
R	1.4968319567309	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	13800y1 110400hu1 82800bi1 1104e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600c1

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

---

Quadratic twists for elliptic curve 27600c1

-4	8	-3	5
13800y1	110400hu1	82800bi1	1104e1

---

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