Cremona's table of elliptic curves

7943 = 13² · 47

Field	Data	Notes
Atkin-Lehner	13+ 47+	Signs for the Atkin-Lehner involutions
Class	7943a	Isogeny class
Conductor	7943	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	35880	Modular degree for the optimal curve
Δ	-304529408494441 = -1 · 1310 · 472	Discriminant
Eigenvalues	1  2 -3  4 -2 13+  7 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,13686,-564559]	[a1,a2,a3,a4,a6]
Generators	[5800128:43021427:132651]	Generators of the group modulo torsion
j	2056223/2209	j-invariant
L	6.41274687944	L(r)(E,1)/r!
Ω	0.29498025530983	Real period
R	10.869790035106	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	127088o1 71487p1 7943b1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 7943a1

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	-3	4	-2	+	7	-2	0	-9	-2	-1	-1	4	+	9	4	1	-8	-8	-1	-8	-14	-6	-14

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Quadratic twists for elliptic curve 7943a1

-4	-3	13
127088o1	71487p1	7943b1

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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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