Cremona's table of elliptic curves

4270 = 2 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 61-	Signs for the Atkin-Lehner involutions
Class	4270h	Isogeny class
Conductor	4270	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	28132228880 = 24 · 5 · 78 · 61	Discriminant
Eigenvalues	2-  0 5- 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-26077,-1614251]	[a1,a2,a3,a4,a6]
j	1961015288853854241/28132228880	j-invariant
L	3.005569741764	L(r)(E,1)/r!
Ω	0.3756962177205	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34160bd4 38430g4 21350g4 29890m4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4270h3

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
-	0	-	+	0	-2	2	4	0	6	4	6	-6	-4	4	6	0	-	12	4	2	-4	8	18	10

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Quadratic twists for elliptic curve 4270h3

-4	-3	5	-7
34160bd4	38430g4	21350g4	29890m4

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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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