Cremona's table of elliptic curves

3894 = 2 · 3 · 11 · 59

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 59-	Signs for the Atkin-Lehner involutions
Class	3894k	Isogeny class
Conductor	3894	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	28800	Modular degree for the optimal curve
Δ	14574821572608 = 220 · 3 · 113 · 592	Discriminant
Eigenvalues	2- 3+  2 -4 11+  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-289917,59962899]	[a1,a2,a3,a4,a6]
Generators	[-201:10596:1]	Generators of the group modulo torsion
j	2694913635715921176913/14574821572608	j-invariant
L	4.5900445064528	L(r)(E,1)/r!
Ω	0.62332115360352	Real period
R	2.9455406606479	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	31152bd1 124608br1 11682h1 97350x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3894k1

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

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Quadratic twists for elliptic curve 3894k1

-4	8	-3	5	-11
31152bd1	124608br1	11682h1	97350x1	42834j1

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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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