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	12	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-364544 = -1 · 212 · 89	Discriminant
Eigenvalues	2-  1  3 -4 -6  2  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,6,-28]	[a1,a2,a3,a4,a6]
j	23639903/364544	j-invariant
L	1.9680331227476	L(r)(E,1)/r!
Ω	1.4760248420607	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	1424c1 5696b1 1602b1 4450b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 178a1

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

---

Quadratic twists for elliptic curve 178a1

-4	8	-3	5	-7	-11	13	17	-19	-23	89
1424c1	5696b1	1602b1	4450b1	8722o1	21538a1	30082d1	51442f1	64258b1	94162r1	15842b1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations