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	40	Product of Tamagawa factors cp
Δ	-651987351562500000 = -1 · 25 · 34 · 512 · 1013	Discriminant
Eigenvalues	2- 3- 5+ -1  0 -4 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-224331,-56425455]	[a1,a2,a3,a4,a6]
Generators	[1368:46191:1]	Generators of the group modulo torsion
j	-1248509093938624216369/651987351562500000	j-invariant
L	5.1734512856945	L(r)(E,1)/r!
Ω	0.10705587817149	Real period
R	1.2081193891584	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24240r2 96960r2 9090k2 15150a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3030r2

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 3030r2

-4	8	-3	5
24240r2	96960r2	9090k2	15150a2

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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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