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	3978a	Isogeny class
Conductor	3978	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	11118036713472 = 216 · 310 · 132 · 17	Discriminant
Eigenvalues	2+ 3-  0 -2  2 13+ 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-10242,-362732]	[a1,a2,a3,a4,a6]
j	162995025390625/15251079168	j-invariant
L	0.95483500139483	L(r)(E,1)/r!
Ω	0.47741750069742	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	31824t1 127296w1 1326d1 99450di1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3978a1

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

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Quadratic twists for elliptic curve 3978a1

-4	8	-3	5	13	17
31824t1	127296w1	1326d1	99450di1	51714n1	67626d1

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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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