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	8624t	Isogeny class
Conductor	8624	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	21504	Modular degree for the optimal curve
Δ	-79999573147648 = -1 · 214 · 79 · 112	Discriminant
Eigenvalues	2-  2 -2 7- 11+  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,10176,167168]	[a1,a2,a3,a4,a6]
Generators	[146:2178:1]	Generators of the group modulo torsion
j	704969/484	j-invariant
L	5.3387074483091	L(r)(E,1)/r!
Ω	0.38459856981758	Real period
R	3.4703115581275	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	1078m1 34496dn1 77616gg1 8624v1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624t1

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 8624t1

-4	8	-3	-7	-11
1078m1	34496dn1	77616gg1	8624v1	94864ct1

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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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