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	4	Product of Tamagawa factors cp
Δ	933897762 = 2 · 34 · 78	Discriminant
Eigenvalues	2- 3+ -2 7+ -4  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-914,-10915]	[a1,a2,a3,a4,a6]
j	84448510979617/933897762	j-invariant
L	0.8688618643742	L(r)(E,1)/r!
Ω	0.8688618643742	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	336d5 1344g5 126b5 1050h5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 42a5

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 42a5

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
336d5	1344g5	126b5	1050h5	294c5	5082i5	7098b5	12138bb5	15162l5	22218z6	35322p6	40362bc6	57498b6	70602bn6	77658t6	92778m6	117978f6

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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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