Cremona's table of elliptic curves

2130 = 2 · 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 71+	Signs for the Atkin-Lehner involutions
Class	2130k	Isogeny class
Conductor	2130	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	6669041561640 = 23 · 38 · 5 · 714	Discriminant
Eigenvalues	2- 3+ 5- -4  0 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-8720,284105]	[a1,a2,a3,a4,a6]
Generators	[75:205:1]	Generators of the group modulo torsion
j	73329087328692481/6669041561640	j-invariant
L	3.7021822073901	L(r)(E,1)/r!
Ω	0.73023988295806	Real period
R	1.6899388332472	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	17040bc4 68160ba3 6390j4 10650h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2130k3

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
-	+	-	-4	0	-2	-2	4	4	-10	0	-10	-6	-4	-4	-2	-8	-6	-4	+	-6	16	-12	10	-2

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Quadratic twists for elliptic curve 2130k3

-4	8	-3	5	-7
17040bc4	68160ba3	6390j4	10650h3	104370dc3

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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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