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	8970m	Isogeny class
Conductor	8970	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-11334492000000 = -1 · 28 · 36 · 56 · 132 · 23	Discriminant
Eigenvalues	2- 3+ 5-  0  2 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,5615,5615]	[a1,a2,a3,a4,a6]
Generators	[103:-1352:1]	Generators of the group modulo torsion
j	19577992591125359/11334492000000	j-invariant
L	5.9556413055138	L(r)(E,1)/r!
Ω	0.4295017028716	Real period
R	0.28888327962842	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	71760by1 26910l1 44850z1 116610a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8970m1

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

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Quadratic twists for elliptic curve 8970m1

-4	-3	5	13
71760by1	26910l1	44850z1	116610a1

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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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