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
deg	3072	Modular degree for the optimal curve
Δ	-10624768 = -1 · 28 · 73 · 112	Discriminant
Eigenvalues	2+  2 -4 7- 11+ -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-100,-384]	[a1,a2,a3,a4,a6]
j	-1272112/121	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	4312l1 34496dq1 77616cq1 8624d1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624c1

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 8624c1

-4	8	-3	-7	-11
4312l1	34496dq1	77616cq1	8624d1	94864w1

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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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