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	8624c	Isogeny class
Conductor	8624	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3863552 = 210 · 73 · 11	Discriminant
Eigenvalues	2+  2 -4 7- 11+ -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1640,-25024]	[a1,a2,a3,a4,a6]
j	1389715708/11	j-invariant
L	1.5003643245834	L(r)(E,1)/r!
Ω	0.7501821622917	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4312l2 34496dq2 77616cq2 8624d2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624c2

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

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Quadratic twists for elliptic curve 8624c2

-4	8	-3	-7	-11
4312l2	34496dq2	77616cq2	8624d2	94864w2

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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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