Cremona's table of elliptic curves

8624 = 2⁴ · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	8624k	Isogeny class
Conductor	8624	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	64934718464 = 210 · 78 · 11	Discriminant
Eigenvalues	2+ -2 -2 7- 11- -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11384,-471164]	[a1,a2,a3,a4,a6]
Generators	[135:686:1]	Generators of the group modulo torsion
j	1354435492/539	j-invariant
L	2.1852836973941	L(r)(E,1)/r!
Ω	0.46220328322928	Real period
R	2.363985476397	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	4312d2 34496cs2 77616br2 1232c2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624k2

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

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Quadratic twists for elliptic curve 8624k2

-4	8	-3	-7	-11
4312d2	34496cs2	77616br2	1232c2	94864y2

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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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