Cremona's table of elliptic curves

24745 = 5 · 7² · 101

Field	Data	Notes
Atkin-Lehner	5- 7- 101+	Signs for the Atkin-Lehner involutions
Class	24745f	Isogeny class
Conductor	24745	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	571648	Modular degree for the optimal curve
Δ	-20996062631082035 = -1 · 5 · 79 · 1014	Discriminant
Eigenvalues	2 -3 5- 7- -3  1  7 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-129997,19340655]	[a1,a2,a3,a4,a6]
Generators	[2450:22977:8]	Generators of the group modulo torsion
j	-6020621733888/520302005	j-invariant
L	6.3461420436295	L(r)(E,1)/r!
Ω	0.37499507973114	Real period
R	4.2308168737704	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	123725j1 24745e1	Quadratic twists by: 5 -7

Hecke Eigenvalues for elliptic curve 24745f1

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	-3	-	-	-3	1	7	-6	-4	3	-2	8	10	-6	-3	-6	10	-4	-2	0	2	-1	12	12	3

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Quadratic twists for elliptic curve 24745f1

5	-7
123725j1	24745e1

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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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