Cremona's table of elliptic curves

100800 = 2⁶ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	100800jq	Isogeny class
Conductor	100800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	60480000000 = 212 · 33 · 57 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0 -2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3300,72000]	[a1,a2,a3,a4,a6]
Generators	[60:-300:1]	Generators of the group modulo torsion
j	2299968/35	j-invariant
L	6.6888376410978	L(r)(E,1)/r!
Ω	1.1119750498523	Real period
R	0.75190959139326	Regulator
r	1	Rank of the group of rational points
S	0.99999999971686	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800iq1 50400cj1 100800jp1 20160dc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800jq1

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	-4	2	4	-6	0	4	-6	10	2	-10	4	-4	-14	6	-10	-8	16	2	2

---

Quadratic twists for elliptic curve 100800jq1

-4	8	-3	5
100800iq1	50400cj1	100800jp1	20160dc1

---

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