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	3894b	Isogeny class
Conductor	3894	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	120907017792 = 26 · 37 · 114 · 59	Discriminant
Eigenvalues	2+ 3+  0  0 11-  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2365,-41987]	[a1,a2,a3,a4,a6]
Generators	[-33:55:1]	Generators of the group modulo torsion
j	1463875168353625/120907017792	j-invariant
L	2.3474590344678	L(r)(E,1)/r!
Ω	0.68816462798994	Real period
R	1.7055940824251	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31152v1 124608x1 11682o1 97350cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3894b1

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

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Quadratic twists for elliptic curve 3894b1

-4	8	-3	5	-11
31152v1	124608x1	11682o1	97350cv1	42834x1

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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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