Cremona's table of elliptic curves

4624 = 2⁴ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	4624b	Isogeny class
Conductor	4624	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8704	Modular degree for the optimal curve
Δ	30358496383232 = 28 · 179	Discriminant
Eigenvalues	2+  2  0 -2 -2 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8188,107904]	[a1,a2,a3,a4,a6]
Generators	[9540:38728:729]	Generators of the group modulo torsion
j	2000	j-invariant
L	4.7841310348128	L(r)(E,1)/r!
Ω	0.58512370814795	Real period
R	8.1762727576972	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	2312b1 18496s1 41616t1 115600j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4624b1

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	-2	+	4	6	8	-6	-8	0	-12	8	-6	4	8	-4	-6	-8	-2	-4	-14	-8

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Quadratic twists for elliptic curve 4624b1

-4	8	-3	5	17
2312b1	18496s1	41616t1	115600j1	4624c1

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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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