Cremona's table of elliptic curves

19698 = 2 · 3 · 7² · 67

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 67+	Signs for the Atkin-Lehner involutions
Class	19698a	Isogeny class
Conductor	19698	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	160927491677683248 = 24 · 312 · 710 · 67	Discriminant
Eigenvalues	2+ 3+  2 7- -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-316614,-65931228]	[a1,a2,a3,a4,a6]
j	29835131673951577/1367861109552	j-invariant
L	0.80734243452003	L(r)(E,1)/r!
Ω	0.20183560863001	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	59094bt3 2814a4	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 19698a3

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

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Quadratic twists for elliptic curve 19698a3

-3	-7
59094bt3	2814a4

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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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