Cremona's table of elliptic curves

3198 = 2 · 3 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 41-	Signs for the Atkin-Lehner involutions
Class	3198a	Isogeny class
Conductor	3198	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	14080	Modular degree for the optimal curve
Δ	43147377342576 = 24 · 311 · 135 · 41	Discriminant
Eigenvalues	2+ 3+  3 -2 -3 13+  5  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9081,101493]	[a1,a2,a3,a4,a6]
j	82832250843593497/43147377342576	j-invariant
L	1.1287416783052	L(r)(E,1)/r!
Ω	0.56437083915259	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25584v1 102336bj1 9594r1 79950cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3198a1

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
+	+	3	-2	-3	+	5	4	-9	3	-7	4	-	6	3	11	8	15	8	-8	-4	-13	12	-10	15

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Quadratic twists for elliptic curve 3198a1

-4	8	-3	5	13
25584v1	102336bj1	9594r1	79950cb1	41574n1

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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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