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	16	Product of Tamagawa factors cp
Δ	-23402547 = -1 · 33 · 74 · 192	Discriminant
Eigenvalues	1 3+  0 7-  2 -6 -8 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-42,-245]	[a1,a2,a3,a4,a6]
Generators	[14:35:1]	Generators of the group modulo torsion
j	-307546875/866761	j-invariant
L	3.1370129085151	L(r)(E,1)/r!
Ω	0.86811242794337	Real period
R	0.9034005295682	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	19152bf2 76608j2 1197b2 29925d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1197a2

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 1197a2

-4	8	-3	5	-7	-19
19152bf2	76608j2	1197b2	29925d2	8379a2	22743i2

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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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