Cremona's table of elliptic curves

1005 = 3 · 5 · 67

Field	Data	Notes
Atkin-Lehner	3- 5+ 67-	Signs for the Atkin-Lehner involutions
Class	1005b	Isogeny class
Conductor	1005	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-380653171875 = -1 · 34 · 56 · 673	Discriminant
Eigenvalues	0 3- 5+  2 -6  2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3001,-70904]	[a1,a2,a3,a4,a6]
Generators	[542:12562:1]	Generators of the group modulo torsion
j	-2989967081734144/380653171875	j-invariant
L	2.400311923811	L(r)(E,1)/r!
Ω	0.32023041220063	Real period
R	0.3123157358421	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16080n2 64320i2 3015c2 5025a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1005b2

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	-	+	2	-6	2	-3	-1	-9	3	-4	-7	6	-10	9	-12	-15	8	-	-12	11	-4	-12	15	2

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Quadratic twists for elliptic curve 1005b2

-4	8	-3	5	-7	-11	-67
16080n2	64320i2	3015c2	5025a2	49245q2	121605k2	67335e2

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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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