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	4270g	Isogeny class
Conductor	4270	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	20837600 = 25 · 52 · 7 · 612	Discriminant
Eigenvalues	2- -2 5+ 7-  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1201,-16119]	[a1,a2,a3,a4,a6]
Generators	[-20:11:1]	Generators of the group modulo torsion
j	191591101730449/20837600	j-invariant
L	3.7194458823299	L(r)(E,1)/r!
Ω	0.81098860801135	Real period
R	0.91726217744303	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	34160l2 38430u2 21350b2 29890ba2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4270g2

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
-	-2	+	-	0	-2	2	4	-8	-8	4	6	-6	4	8	-6	-10	+	-12	6	4	-10	-14	-12	16

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Quadratic twists for elliptic curve 4270g2

-4	-3	5	-7
34160l2	38430u2	21350b2	29890ba2

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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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