Cremona's table of elliptic curves

178 = 2 · 89

Field	Data	Notes
Atkin-Lehner	2- 89+	Signs for the Atkin-Lehner involutions
Class	178a	Isogeny class
Conductor	178	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-11279504 = -1 · 24 · 893	Discriminant
Eigenvalues	2-  1  3 -4 -6  2  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-554,-5068]	[a1,a2,a3,a4,a6]
j	-18806241149857/11279504	j-invariant
L	1.9680331227476	L(r)(E,1)/r!
Ω	0.4920082806869	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1424c2 5696b2 1602b2 4450b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 178a2

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	3	-4	-6	2	3	5	-3	0	5	-10	0	-1	12	9	12	-10	-4	-6	-1	-10	-12	+	17

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Quadratic twists for elliptic curve 178a2

-4	8	-3	5	-7	-11	13	17	-19	-23	89
1424c2	5696b2	1602b2	4450b2	8722o2	21538a2	30082d2	51442f2	64258b2	94162r2	15842b2

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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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