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	8624h	Isogeny class
Conductor	8624	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	60368 = 24 · 73 · 11	Discriminant
Eigenvalues	2+  2  0 7- 11-  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-23,-34]	[a1,a2,a3,a4,a6]
Generators	[714:3536:27]	Generators of the group modulo torsion
j	256000/11	j-invariant
L	6.055253412796	L(r)(E,1)/r!
Ω	2.1779945405166	Real period
R	5.560393564035	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	4312j1 34496cu1 77616bh1 8624j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624h1

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	0	-	-	2	-2	-4	0	-6	-2	-2	6	0	-6	2	2	-2	4	0	-6	-12	-4	-8	12

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Quadratic twists for elliptic curve 8624h1

-4	8	-3	-7	-11
4312j1	34496cu1	77616bh1	8624j1	94864t1

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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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