Cremona's table of elliptic curves

4730 = 2 · 5 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2+ 5- 11+ 43-	Signs for the Atkin-Lehner involutions
Class	4730b	Isogeny class
Conductor	4730	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	524098606240000 = 28 · 54 · 116 · 432	Discriminant
Eigenvalues	2+  0 5-  0 11+  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-31174,-1801932]	[a1,a2,a3,a4,a6]
Generators	[652:15634:1]	Generators of the group modulo torsion
j	3350496292255693881/524098606240000	j-invariant
L	2.9248175557468	L(r)(E,1)/r!
Ω	0.36308114235138	Real period
R	4.0277739802253	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	37840bb2 42570x2 23650l2 52030x2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4730b2

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

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Quadratic twists for elliptic curve 4730b2

-4	-3	5	-11
37840bb2	42570x2	23650l2	52030x2

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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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