Cremona's table of elliptic curves

8970 = 2 · 3 · 5 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 13- 23+	Signs for the Atkin-Lehner involutions
Class	8970c	Isogeny class
Conductor	8970	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	117869029200 = 24 · 34 · 52 · 13 · 234	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-27832,-1798736]	[a1,a2,a3,a4,a6]
Generators	[-97:56:1]	Generators of the group modulo torsion
j	2384412229264108681/117869029200	j-invariant
L	3.0200838638115	L(r)(E,1)/r!
Ω	0.36962616565204	Real period
R	2.0426610346185	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	71760cd4 26910bf4 44850bu4 116610bl4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8970c3

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

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Quadratic twists for elliptic curve 8970c3

-4	-3	5	13
71760cd4	26910bf4	44850bu4	116610bl4

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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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