Cremona's table of elliptic curves

42 = 2 · 3 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+	Signs for the Atkin-Lehner involutions
Class	42a	Isogeny class
Conductor	42	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	63011844 = 22 · 38 · 74	Discriminant
Eigenvalues	2- 3+ -2 7+ -4  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-104,101]	[a1,a2,a3,a4,a6]
j	124475734657/63011844	j-invariant
L	0.8688618643742	L(r)(E,1)/r!
Ω	1.7377237287484	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	336d4 1344g3 126b4 1050h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 42a3

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

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Quadratic twists for elliptic curve 42a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
336d4	1344g3	126b4	1050h3	294c4	5082i4	7098b3	12138bb3	15162l4	22218z3	35322p3	40362bc3	57498b3	70602bn3	77658t3	92778m3	117978f3

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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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