Cremona's table of elliptic curves

3978 = 2 · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	3978b	Isogeny class
Conductor	3978	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3660027862608 = 24 · 36 · 13 · 176	Discriminant
Eigenvalues	2+ 3-  4 -2  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-10905,-425827]	[a1,a2,a3,a4,a6]
j	196741326427281/5020614352	j-invariant
L	1.8716611841904	L(r)(E,1)/r!
Ω	0.46791529604761	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	31824y2 127296bi2 442b2 99450dh2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3978b2

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
+	-	4	-2	2	+	+	0	4	-2	-2	0	0	4	8	6	-8	-2	16	14	-16	8	12	18	-4

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Quadratic twists for elliptic curve 3978b2

-4	8	-3	5	13	17
31824y2	127296bi2	442b2	99450dh2	51714r2	67626m2

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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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