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	8624v	Isogeny class
Conductor	8624	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	41139101696 = 213 · 73 · 114	Discriminant
Eigenvalues	2- -2  2 7- 11+ -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-912,-4460]	[a1,a2,a3,a4,a6]
Generators	[-12:70:1]	Generators of the group modulo torsion
j	59776471/29282	j-invariant
L	3.2650498050632	L(r)(E,1)/r!
Ω	0.91295371450125	Real period
R	1.7881792653896	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	1078l2 34496dk2 77616go2 8624t2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624v2

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	-	+	-2	0	-2	0	6	4	2	-8	-12	12	-2	10	10	12	-4	-12	0	-18	0	12

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Quadratic twists for elliptic curve 8624v2

-4	8	-3	-7	-11
1078l2	34496dk2	77616go2	8624t2	94864da2

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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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