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	1178d	Isogeny class
Conductor	1178	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	36518 = 2 · 19 · 312	Discriminant
Eigenvalues	2- -2  2  0 -4 -6 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-202,-1122]	[a1,a2,a3,a4,a6]
Generators	[134:63:8]	Generators of the group modulo torsion
j	911826451873/36518	j-invariant
L	2.9168605449295	L(r)(E,1)/r!
Ω	1.266343596847	Real period
R	4.6067442551802	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9424d2 37696a2 10602e2 29450g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1178d2

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	-4	-6	-6	-	6	-6	+	6	-6	-12	0	2	12	8	0	-8	-10	8	-16	-8	-10

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Quadratic twists for elliptic curve 1178d2

-4	8	-3	5	-7	-19	-31
9424d2	37696a2	10602e2	29450g2	57722q2	22382d2	36518h2

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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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