Cremona's table of elliptic curves

22785 = 3 · 5 · 7² · 31

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 31-	Signs for the Atkin-Lehner involutions
Class	22785d	Isogeny class
Conductor	22785	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-241423095703125 = -1 · 3 · 512 · 73 · 312	Discriminant
Eigenvalues	-1 3+ 5+ 7- -4  2  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-70526,7218224]	[a1,a2,a3,a4,a6]
Generators	[181:560:1]	Generators of the group modulo torsion
j	-113103940375249543/703857421875	j-invariant
L	2.3827112484718	L(r)(E,1)/r!
Ω	0.55892963749188	Real period
R	2.1314948149501	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	68355bf2 113925cj2 22785r2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 22785d2

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
-1	+	+	-	-4	2	2	8	4	-8	-	-10	-2	10	10	12	-6	-2	-8	-8	-10	-14	12	6	-12

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Quadratic twists for elliptic curve 22785d2

-3	5	-7
68355bf2	113925cj2	22785r2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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