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	1178c	Isogeny class
Conductor	1178	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-146072 = -1 · 23 · 19 · 312	Discriminant
Eigenvalues	2- -1  2 -5  4 -5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,13,9]	[a1,a2,a3,a4,a6]
Generators	[9:26:1]	Generators of the group modulo torsion
j	241804367/146072	j-invariant
L	3.1331011093662	L(r)(E,1)/r!
Ω	2.0009765949532	Real period
R	0.26096433088959	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9424e1 37696i1 10602d1 29450d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1178c1

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	2	-5	4	-5	-3	+	-3	-5	-	-10	0	12	-12	-5	1	6	-11	8	3	-6	-6	0	-10

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Quadratic twists for elliptic curve 1178c1

-4	8	-3	5	-7	-19	-31
9424e1	37696i1	10602d1	29450d1	57722t1	22382b1	36518c1

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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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