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	8970o	Isogeny class
Conductor	8970	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	177258546707130720 = 25 · 310 · 5 · 138 · 23	Discriminant
Eigenvalues	2- 3+ 5-  0 -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1158935635,-15186262361743]	[a1,a2,a3,a4,a6]
Generators	[155648955:-104624879612:343]	Generators of the group modulo torsion
j	172147873551890383480309150814641/177258546707130720	j-invariant
L	5.8349690388324	L(r)(E,1)/r!
Ω	0.025875260185559	Real period
R	11.275189113053	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	71760cc6 26910p6 44850r6 116610e6	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8970o5

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

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Quadratic twists for elliptic curve 8970o5

-4	-3	5	13
71760cc6	26910p6	44850r6	116610e6

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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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