Cremona's table of elliptic curves

5824 = 2⁶ · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	5824a	Isogeny class
Conductor	5824	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-251969536 = -1 · 214 · 7 · 133	Discriminant
Eigenvalues	2+  0  1 7+ -2 13+  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-272,-1888]	[a1,a2,a3,a4,a6]
Generators	[2405:121:125]	Generators of the group modulo torsion
j	-135834624/15379	j-invariant
L	3.8459352574426	L(r)(E,1)/r!
Ω	0.58407461593648	Real period
R	6.5846642749166	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5824y1 728c1 52416bn1 40768be1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5824a1

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
+	0	1	+	-2	+	0	7	-3	9	5	8	-10	-5	7	-3	0	-6	10	4	-11	-11	-11	-3	-15

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Quadratic twists for elliptic curve 5824a1

-4	8	-3	-7	13
5824y1	728c1	52416bn1	40768be1	75712w1

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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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