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	1197a	Isogeny class
Conductor	1197	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	25137 = 33 · 72 · 19	Discriminant
Eigenvalues	1 3+  0 7-  2 -6 -8 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-57,-152]	[a1,a2,a3,a4,a6]
Generators	[12:22:1]	Generators of the group modulo torsion
j	766060875/931	j-invariant
L	3.1370129085151	L(r)(E,1)/r!
Ω	1.7362248558867	Real period
R	1.8068010591364	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	19152bf1 76608j1 1197b1 29925d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1197a1

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

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Quadratic twists for elliptic curve 1197a1

-4	8	-3	5	-7	-19
19152bf1	76608j1	1197b1	29925d1	8379a1	22743i1

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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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