Cremona's table of elliptic curves

1947 = 3 · 11 · 59

Field	Data	Notes
Atkin-Lehner	3+ 11- 59+	Signs for the Atkin-Lehner involutions
Class	1947c	Isogeny class
Conductor	1947	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	264	Modular degree for the optimal curve
Δ	2591457 = 3 · 114 · 59	Discriminant
Eigenvalues	-1 3+ -2  0 11-  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-44,-100]	[a1,a2,a3,a4,a6]
j	9434056897/2591457	j-invariant
L	0.47294230859863	L(r)(E,1)/r!
Ω	1.8917692343945	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	31152z1 124608bg1 5841f1 48675q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1947c1

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
-1	+	-2	0	-	2	-2	-4	0	2	-8	6	6	-8	0	-10	+	10	-4	16	6	-8	12	10	10

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Quadratic twists for elliptic curve 1947c1

-4	8	-3	5	-7	-11	-59
31152z1	124608bg1	5841f1	48675q1	95403l1	21417a1	114873b1

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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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