Cremona's table of elliptic curves

4774 = 2 · 7 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 7- 11+ 31-	Signs for the Atkin-Lehner involutions
Class	4774b	Isogeny class
Conductor	4774	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	-6303360448 = -1 · 26 · 7 · 114 · 312	Discriminant
Eigenvalues	2+  2 -4 7- 11+  0  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-182,3860]	[a1,a2,a3,a4,a6]
Generators	[52:346:1]	Generators of the group modulo torsion
j	-672451615081/6303360448	j-invariant
L	3.1180444062865	L(r)(E,1)/r!
Ω	1.1440940319601	Real period
R	1.3626696404249	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	38192q1 42966bk1 119350bg1 33418k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4774b1

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

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Quadratic twists for elliptic curve 4774b1

-4	-3	5	-7	-11
38192q1	42966bk1	119350bg1	33418k1	52514u1

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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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