Cremona's table of elliptic curves

4305 = 3 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	4305h	Isogeny class
Conductor	4305	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-98117633620125 = -1 · 34 · 53 · 78 · 412	Discriminant
Eigenvalues	-1 3- 5+ 7- -2 -4  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-17791,1028750]	[a1,a2,a3,a4,a6]
Generators	[101:-565:1]	Generators of the group modulo torsion
j	-622768040074052209/98117633620125	j-invariant
L	2.6132599178106	L(r)(E,1)/r!
Ω	0.57808085527895	Real period
R	0.28253615972863	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	68880bf2 12915s2 21525b2 30135r2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4305h2

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

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Quadratic twists for elliptic curve 4305h2

-4	-3	5	-7
68880bf2	12915s2	21525b2	30135r2

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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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