Cremona's table of elliptic curves

1197 = 3² · 7 · 19

Field	Data	Notes
Atkin-Lehner	3- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	1197d	Isogeny class
Conductor	1197	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	395982180657 = 311 · 76 · 19	Discriminant
Eigenvalues	-1 3-  0 7+  2 -4  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1895,10014]	[a1,a2,a3,a4,a6]
j	1031831907625/543185433	j-invariant
L	0.8326732402379	L(r)(E,1)/r!
Ω	0.8326732402379	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19152by1 76608br1 399a1 29925ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1197d1

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	-	0	+	2	-4	4	+	-2	2	0	6	6	8	0	2	-4	-10	14	12	10	10	12	6	-4

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Quadratic twists for elliptic curve 1197d1

-4	8	-3	5	-7	-19
19152by1	76608br1	399a1	29925ba1	8379m1	22743m1

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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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