Cremona's table of elliptic curves

4270 = 2 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7- 61+	Signs for the Atkin-Lehner involutions
Class	4270a	Isogeny class
Conductor	4270	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	8369200 = 24 · 52 · 73 · 61	Discriminant
Eigenvalues	2+ -3 5+ 7- -3 -6 -7 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-70,196]	[a1,a2,a3,a4,a6]
Generators	[-8:18:1] [-7:21:1]	Generators of the group modulo torsion
j	38238692409/8369200	j-invariant
L	2.278332997793	L(r)(E,1)/r!
Ω	2.1955378194789	Real period
R	0.086475888260783	Regulator
r	2	Rank of the group of rational points
S	0.9999999999991	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34160m1 38430bq1 21350q1 29890j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4270a1

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
+	-3	+	-	-3	-6	-7	-5	5	-4	-2	-2	-6	-11	-9	10	6	+	-7	7	-14	-1	-15	7	-2

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Quadratic twists for elliptic curve 4270a1

-4	-3	5	-7
34160m1	38430bq1	21350q1	29890j1

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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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