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	3894a	Isogeny class
Conductor	3894	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	350896128 = 214 · 3 · 112 · 59	Discriminant
Eigenvalues	2+ 3+  4 -4 11+ -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-403,-3155]	[a1,a2,a3,a4,a6]
j	7266438420409/350896128	j-invariant
L	1.0683946932429	L(r)(E,1)/r!
Ω	1.0683946932429	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	31152bf1 124608bt1 11682u1 97350co1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3894a1

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	-4	+	-4	6	-4	0	0	-6	-4	6	-8	8	8	-	0	12	14	2	-4	12	10	-2

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Quadratic twists for elliptic curve 3894a1

-4	8	-3	5	-11
31152bf1	124608bt1	11682u1	97350co1	42834bb1

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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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