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	1947a	Isogeny class
Conductor	1947	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1263603 = 3 · 112 · 592	Discriminant
Eigenvalues	1 3+  2  2 11+ -2  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-29,-42]	[a1,a2,a3,a4,a6]
j	2845178713/1263603	j-invariant
L	2.1342615328881	L(r)(E,1)/r!
Ω	2.1342615328881	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	31152bc2 124608bo2 5841i2 48675n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1947a2

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

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Quadratic twists for elliptic curve 1947a2

-4	8	-3	5	-7	-11	-59
31152bc2	124608bo2	5841i2	48675n2	95403h2	21417e2	114873f2

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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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