Cremona's table of elliptic curves

3030 = 2 · 3 · 5 · 101

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 101+	Signs for the Atkin-Lehner involutions
Class	3030r	Isogeny class
Conductor	3030	Conductor
∏ cp	360	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-1099275079680000 = -1 · 215 · 312 · 54 · 101	Discriminant
Eigenvalues	2- 3- 5+ -1  0 -4 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,21909,995121]	[a1,a2,a3,a4,a6]
Generators	[-24:687:1]	Generators of the group modulo torsion
j	1163027916345872591/1099275079680000	j-invariant
L	5.1734512856945	L(r)(E,1)/r!
Ω	0.32116763451448	Real period
R	0.4027064630528	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	24240r1 96960r1 9090k1 15150a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3030r1

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	0	-4	-3	-7	-6	-3	8	-4	-12	-1	6	9	0	5	2	-6	-4	-10	0	12	17

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Quadratic twists for elliptic curve 3030r1

-4	8	-3	5
24240r1	96960r1	9090k1	15150a1

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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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