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	6	Product of Tamagawa factors cp
deg	2832	Modular degree for the optimal curve
Δ	729080489737 = 374 · 733	Discriminant
Eigenvalues	1  0 -2  2 -2 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-7648,256059]	[a1,a2,a3,a4,a6]
j	49476536631111897/729080489737	j-invariant
L	1.3557682608343	L(r)(E,1)/r!
Ω	0.90384550722288	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	43216a1 24309e1 67525a1 99937c1	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 2701a1

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 2701a1

-4	-3	5	37
43216a1	24309e1	67525a1	99937c1

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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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