Cremona's table of elliptic curves

28272 = 2⁴ · 3 · 19 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 19- 31+	Signs for the Atkin-Lehner involutions
Class	28272f	Isogeny class
Conductor	28272	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	42068736 = 28 · 32 · 19 · 312	Discriminant
Eigenvalues	2- 3+  2 -4 -4  4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-132,540]	[a1,a2,a3,a4,a6]
Generators	[-3:30:1]	Generators of the group modulo torsion
j	1001132368/164331	j-invariant
L	4.0515197255065	L(r)(E,1)/r!
Ω	1.9429684903631	Real period
R	2.0852215286051	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	7068e2 113088bc2 84816s2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 28272f2

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

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Quadratic twists for elliptic curve 28272f2

-4	8	-3
7068e2	113088bc2	84816s2

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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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