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	3978j	Isogeny class
Conductor	3978	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	4247477676 = 22 · 37 · 134 · 17	Discriminant
Eigenvalues	2- 3-  2  0  0 13- 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-9824,-372297]	[a1,a2,a3,a4,a6]
j	143820170742457/5826444	j-invariant
L	3.8363830424837	L(r)(E,1)/r!
Ω	0.47954788031046	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	31824bj4 127296g4 1326b4 99450v4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3978j3

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

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Quadratic twists for elliptic curve 3978j3

-4	8	-3	5	13	17
31824bj4	127296g4	1326b4	99450v4	51714d4	67626bd4

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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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