Cremona's table of elliptic curves

1178 = 2 · 19 · 31

Field	Data	Notes
Atkin-Lehner	2- 19+ 31+	Signs for the Atkin-Lehner involutions
Class	1178b	Isogeny class
Conductor	1178	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-210927968 = -1 · 25 · 193 · 312	Discriminant
Eigenvalues	2-  3 -2  3  0 -1 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-936,-10805]	[a1,a2,a3,a4,a6]
j	-90597496156497/210927968	j-invariant
L	4.3154518386581	L(r)(E,1)/r!
Ω	0.43154518386581	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	9424g1 37696h1 10602b1 29450b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1178b1

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

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Quadratic twists for elliptic curve 1178b1

-4	8	-3	5	-7	-19	-31
9424g1	37696h1	10602b1	29450b1	57722y1	22382f1	36518g1

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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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