Cremona's table of elliptic curves

43 = Prime conductor

Field	Data	Notes
Atkin-Lehner	43+	Signs for the Atkin-Lehner involutions
Class	43a	Isogeny class
Conductor	43	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-43 = Prime discriminant	Discriminant
Eigenvalues	-2 -2 -4  0  3 -5 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,0,0]	[a1,a2,a3,a4,a6]
Generators	[0:0:1]	Generators of the group modulo torsion
j	-4096/43	j-invariant
L	0.34352397461848	L(r)(E,1)/r!
Ω	5.4686895299676	Real period
R	0.062816507087488	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	688c1 2752c1 387e1 1075d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 43a1

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	-2	-4	0	3	-5	-3	-2	-1	-6	-1	0	5	+	4	-5	-12	2	-3	2	2	-8	15	-4	7

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Quadratic twists for elliptic curve 43a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
688c1	2752c1	387e1	1075d1	2107a1	5203b1	7267a1	12427b1	15523a1	22747d1	36163a1	41323c1	58867b1	72283b1	1849d1	94987b1	120787a1

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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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