Cremona's table of elliptic curves

15840 = 2⁵ · 3² · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	15840l	Isogeny class
Conductor	15840	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	245760	Modular degree for the optimal curve
Δ	-1432379641275000000 = -1 · 26 · 316 · 58 · 113	Discriminant
Eigenvalues	2+ 3- 5+  2 11- -2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-439653,126117848]	[a1,a2,a3,a4,a6]
Generators	[-151:13750:1]	Generators of the group modulo torsion
j	-201440287521417664/30700866796875	j-invariant
L	4.7720406275646	L(r)(E,1)/r!
Ω	0.26022003035995	Real period
R	1.5282069245283	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	15840d1 31680dj2 5280k1 79200eb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 15840l1

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	0	-6	-8	8	4	-6	12	6	0	-2	4	2	-12	16	-2	10	0	-18	-18

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Quadratic twists for elliptic curve 15840l1

-4	8	-3	5
15840d1	31680dj2	5280k1	79200eb1

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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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