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	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	154953347328 = 28 · 36 · 132 · 173	Discriminant
Eigenvalues	2+ 3-  4 -2  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1545,14093]	[a1,a2,a3,a4,a6]
j	559679941521/212556032	j-invariant
L	1.8716611841904	L(r)(E,1)/r!
Ω	0.93583059209522	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	31824y1 127296bi1 442b1 99450dh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3978b1

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 3978b1

-4	8	-3	5	13	17
31824y1	127296bi1	442b1	99450dh1	51714r1	67626m1

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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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