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	16	Product of Tamagawa factors cp
Δ	63504 = 24 · 34 · 72	Discriminant
Eigenvalues	2- 3+ -2 7+ -4  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-84,261]	[a1,a2,a3,a4,a6]
j	65597103937/63504	j-invariant
L	0.8688618643742	L(r)(E,1)/r!
Ω	3.4754474574968	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	336d2 1344g2 126b2 1050h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 42a2

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 42a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
336d2	1344g2	126b2	1050h2	294c2	5082i2	7098b2	12138bb2	15162l2	22218z2	35322p2	40362bc2	57498b2	70602bn2	77658t2	92778m2	117978f2

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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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