Cremona's table of elliptic curves

24480 = 2⁵ · 3² · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	24480w	Isogeny class
Conductor	24480	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-18040536000 = -1 · 26 · 33 · 53 · 174	Discriminant
Eigenvalues	2- 3+ 5+ -2 -2 -4 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-453,7452]	[a1,a2,a3,a4,a6]
Generators	[7:68:1]	Generators of the group modulo torsion
j	-5949419328/10440125	j-invariant
L	3.7996884649082	L(r)(E,1)/r!
Ω	1.0971795481945	Real period
R	0.8657854749391	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	24480b1 48960y1 24480d1 122400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 24480w1

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	-4	-	-4	0	-2	8	4	-4	4	0	6	10	10	8	0	-6	-8	-12	4	14

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Quadratic twists for elliptic curve 24480w1

-4	8	-3	5
24480b1	48960y1	24480d1	122400a1

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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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