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	3198b	Isogeny class
Conductor	3198	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	-102108404736 = -1 · 210 · 33 · 133 · 412	Discriminant
Eigenvalues	2+ 3- -2  2  4 13+  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,798,-12620]	[a1,a2,a3,a4,a6]
j	56300788871783/102108404736	j-invariant
L	1.6694700159783	L(r)(E,1)/r!
Ω	0.5564900053261	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	25584m1 102336o1 9594u1 79950bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3198b1

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	2	4	+	4	0	-8	6	4	8	+	12	-8	2	8	-2	-8	-16	10	16	0	-14	12

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Quadratic twists for elliptic curve 3198b1

-4	8	-3	5	13
25584m1	102336o1	9594u1	79950bh1	41574s1

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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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