Cremona's table of elliptic curves

2074 = 2 · 17 · 61

Field	Data	Notes
Atkin-Lehner	2- 17+ 61-	Signs for the Atkin-Lehner involutions
Class	2074b	Isogeny class
Conductor	2074	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	176	Modular degree for the optimal curve
Δ	-70516 = -1 · 22 · 172 · 61	Discriminant
Eigenvalues	2-  0  1 -1 -1 -5 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7,-13]	[a1,a2,a3,a4,a6]
Generators	[11:28:1]	Generators of the group modulo torsion
j	-33076161/70516	j-invariant
L	4.2529950009958	L(r)(E,1)/r!
Ω	1.3913971878174	Real period
R	0.76415904786813	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	16592a1 66368a1 18666d1 51850e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2074b1

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	1	-1	-1	-5	+	-6	5	6	-8	0	-9	-12	10	10	-9	-	-1	12	-1	17	0	10	-14

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Quadratic twists for elliptic curve 2074b1

-4	8	-3	5	-7	17	61
16592a1	66368a1	18666d1	51850e1	101626z1	35258h1	126514c1

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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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