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	8624q	Isogeny class
Conductor	8624	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-16233679616 = -1 · 28 · 78 · 11	Discriminant
Eigenvalues	2- -1  1 7- 11+  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1045,14729]	[a1,a2,a3,a4,a6]
Generators	[5:98:1]	Generators of the group modulo torsion
j	-4194304/539	j-invariant
L	3.8209929484209	L(r)(E,1)/r!
Ω	1.2004950028642	Real period
R	0.79571196450308	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2156b1 34496dg1 77616ge1 1232g1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624q1

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	1	-	+	4	6	-2	-1	2	-1	-9	-6	-8	-8	10	1	2	-11	-11	14	14	4	-13	9

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Quadratic twists for elliptic curve 8624q1

-4	8	-3	-7	-11
2156b1	34496dg1	77616ge1	1232g1	94864ck1

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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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