Cremona's table of elliptic curves

4970 = 2 · 5 · 7 · 71

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 71+	Signs for the Atkin-Lehner involutions
Class	4970g	Isogeny class
Conductor	4970	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	6175225000000 = 26 · 58 · 72 · 712	Discriminant
Eigenvalues	2-  0 5+ 7+  0 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-6813,182117]	[a1,a2,a3,a4,a6]
j	34968670162461729/6175225000000	j-invariant
L	2.1565787145726	L(r)(E,1)/r!
Ω	0.7188595715242	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	39760o2 44730p2 24850c2 34790w2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4970g2

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
-	0	+	+	0	-2	2	-8	8	6	-8	6	10	-4	0	10	12	14	8	+	-6	-16	0	-6	2

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Quadratic twists for elliptic curve 4970g2

-4	-3	5	-7
39760o2	44730p2	24850c2	34790w2

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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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