Cremona's table of elliptic curves

2701 = 37 · 73

Field	Data	Notes
Atkin-Lehner	37+ 73-	Signs for the Atkin-Lehner involutions
Class	2701a	Isogeny class
Conductor	2701	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-207176555789641 = -1 · 372 · 736	Discriminant
Eigenvalues	1  0 -2  2 -2 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-803,692770]	[a1,a2,a3,a4,a6]
j	-57302627338377/207176555789641	j-invariant
L	1.3557682608343	L(r)(E,1)/r!
Ω	0.45192275361144	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	43216a2 24309e2 67525a2 99937c2	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 2701a2

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
1	0	-2	2	-2	-2	6	0	-4	6	2	+	6	2	6	-14	14	10	8	0	-	4	-6	10	-2

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Quadratic twists for elliptic curve 2701a2

-4	-3	5	37
43216a2	24309e2	67525a2	99937c2

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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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