Cremona's table of elliptic curves

28380 = 2² · 3 · 5 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11- 43+	Signs for the Atkin-Lehner involutions
Class	28380d	Isogeny class
Conductor	28380	Conductor
∏ cp	180	Product of Tamagawa factors cp
deg	69120	Modular degree for the optimal curve
Δ	1351820566800 = 24 · 310 · 52 · 113 · 43	Discriminant
Eigenvalues	2- 3- 5+ -5 11- -2 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3026,30249]	[a1,a2,a3,a4,a6]
Generators	[-56:165:1] [-50:243:1]	Generators of the group modulo torsion
j	191581696009984/84488785425	j-invariant
L	8.2189609288395	L(r)(E,1)/r!
Ω	0.77044794904167	Real period
R	0.059265384645265	Regulator
r	2	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	113520w1 85140n1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 28380d1

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
-	-	+	-5	-	-2	-4	-5	-9	5	-3	-2	-12	+	-5	-13	3	11	-7	-4	-14	4	-2	-18	11

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Quadratic twists for elliptic curve 28380d1

-4	-3
113520w1	85140n1

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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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