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	4	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-44764 = -1 · 22 · 192 · 31	Discriminant
Eigenvalues	2- -2  2  0 -4 -6 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-12,-20]	[a1,a2,a3,a4,a6]
Generators	[12:34:1]	Generators of the group modulo torsion
j	-192100033/44764	j-invariant
L	2.9168605449295	L(r)(E,1)/r!
Ω	1.266343596847	Real period
R	2.3033721275901	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	9424d1 37696a1 10602e1 29450g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1178d1

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 1178d1

-4	8	-3	5	-7	-19	-31
9424d1	37696a1	10602e1	29450g1	57722q1	22382d1	36518h1

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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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