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	4305i	Isogeny class
Conductor	4305	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-18326193568381125 = -1 · 32 · 53 · 78 · 414	Discriminant
Eigenvalues	-1 3- 5- 7+  0  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-78085,-10634578]	[a1,a2,a3,a4,a6]
j	-52653458609244415441/18326193568381125	j-invariant
L	1.6840636215425	L(r)(E,1)/r!
Ω	0.14033863512854	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68880bw3 12915d4 21525h3 30135c3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4305i4

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

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Quadratic twists for elliptic curve 4305i4

-4	-3	5	-7
68880bw3	12915d4	21525h3	30135c3

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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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