Cremona's table of elliptic curves

178 = 2 · 89

Field	Data	Notes
Atkin-Lehner	2+ 89-	Signs for the Atkin-Lehner involutions
Class	178b	Isogeny class
Conductor	178	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1013888 = 27 · 892	Discriminant
Eigenvalues	2+  2  2  0  0 -4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-684,6608]	[a1,a2,a3,a4,a6]
j	35471840526793/1013888	j-invariant
L	1.2901924240049	L(r)(E,1)/r!
Ω	2.5803848480099	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	1424e2 5696h2 1602c2 4450n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 178b2

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

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Quadratic twists for elliptic curve 178b2

-4	8	-3	5	-7	-11	13	17	-19	-23	89
1424e2	5696h2	1602c2	4450n2	8722i2	21538c2	30082h2	51442b2	64258f2	94162e2	15842a2

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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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