Cremona's table of elliptic curves

12495 = 3 · 5 · 7² · 17

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	12495k	Isogeny class
Conductor	12495	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	-4650185476794375 = -1 · 312 · 54 · 77 · 17	Discriminant
Eigenvalues	-1 3- 5+ 7-  4 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,12494,3237611]	[a1,a2,a3,a4,a6]
Generators	[11:1832:1]	Generators of the group modulo torsion
j	1833318007919/39525924375	j-invariant
L	3.2758272790029	L(r)(E,1)/r!
Ω	0.32509654292195	Real period
R	0.41985313674822	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	37485bs3 62475w3 1785h4	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12495k4

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

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Quadratic twists for elliptic curve 12495k4

-3	5	-7
37485bs3	62475w3	1785h4

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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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