Cremona's table of elliptic curves

123 = 3 · 41

Field	Data	Notes
Atkin-Lehner	3+ 41+	Signs for the Atkin-Lehner involutions
Class	123b	Isogeny class
Conductor	123	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	-123 = -1 · 3 · 41	Discriminant
Eigenvalues	0 3+ -2 -4  5 -4 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,1,-1]	[a1,a2,a3,a4,a6]
Generators	[1:0:1]	Generators of the group modulo torsion
j	32768/123	j-invariant
L	0.87207105599518	L(r)(E,1)/r!
Ω	2.9874191592682	Real period
R	0.29191452872947	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	1968m1 7872k1 369a1 3075h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 123b1

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
0	+	-2	-4	5	-4	-5	-2	4	1	-5	-7	+	7	7	-14	-12	-3	-2	-3	13	-2	-2	18	-14

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Quadratic twists for elliptic curve 123b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	41
1968m1	7872k1	369a1	3075h1	6027g1	14883c1	20787b1	35547f1	44403e1	65067d1	103443h1	118203h1	5043c1

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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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