Cremona's table of elliptic curves

8525 = 5² · 11 · 31

Field	Data	Notes
Atkin-Lehner	5+ 11+ 31-	Signs for the Atkin-Lehner involutions
Class	8525a	Isogeny class
Conductor	8525	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	687011767578125 = 511 · 114 · 312	Discriminant
Eigenvalues	-1  2 5+ -4 11+  4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-414713,102613906]	[a1,a2,a3,a4,a6]
j	504831795225826249/43968753125	j-invariant
L	0.97349527774123	L(r)(E,1)/r!
Ω	0.48674763887062	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	76725x2 1705a2 93775e2	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 8525a2

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
-1	2	+	-4	+	4	-4	-4	2	2	-	4	2	-2	-4	-4	-12	10	-12	8	-8	16	-10	6	-6

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Quadratic twists for elliptic curve 8525a2

-3	5	-11
76725x2	1705a2	93775e2

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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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