Cremona's table of elliptic curves

7259 = 7 · 17 · 61

Field	Data	Notes
Atkin-Lehner	7+ 17- 61-	Signs for the Atkin-Lehner involutions
Class	7259b	Isogeny class
Conductor	7259	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	-110542232668931 = -1 · 73 · 175 · 613	Discriminant
Eigenvalues	-1  3  1 7+ -3 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,10908,249442]	[a1,a2,a3,a4,a6]
Generators	[-348:8975:27]	Generators of the group modulo torsion
j	143547761786690799/110542232668931	j-invariant
L	4.5176594729864	L(r)(E,1)/r!
Ω	0.38047499318419	Real period
R	0.79158237359712	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	116144y1 65331g1 50813c1 123403g1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7259b1

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
-1	3	1	+	-3	-2	-	-4	4	9	-2	-5	-9	-8	-12	-12	9	-	10	-1	6	0	-16	-2	5

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Quadratic twists for elliptic curve 7259b1

-4	-3	-7	17
116144y1	65331g1	50813c1	123403g1

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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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