Cremona's table of elliptic curves

3059 = 7 · 19 · 23

Field	Data	Notes
Atkin-Lehner	7+ 19- 23-	Signs for the Atkin-Lehner involutions
Class	3059a	Isogeny class
Conductor	3059	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	704	Modular degree for the optimal curve
Δ	-707158207 = -1 · 7 · 192 · 234	Discriminant
Eigenvalues	-1  0  2 7+  4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-124,-1354]	[a1,a2,a3,a4,a6]
Generators	[1329240:41322767:1331]	Generators of the group modulo torsion
j	-209267191953/707158207	j-invariant
L	2.3373462257301	L(r)(E,1)/r!
Ω	0.65821625928251	Real period
R	7.1020616484859	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	48944s1 27531c1 76475n1 21413c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3059a1

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	+	4	-2	-2	-	-	-2	-4	6	2	-4	-4	-2	0	2	4	-8	2	-16	-4	6	6

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Quadratic twists for elliptic curve 3059a1

-4	-3	5	-7	-19	-23
48944s1	27531c1	76475n1	21413c1	58121a1	70357c1

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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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