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	12495p	Isogeny class
Conductor	12495	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	1160715401488125 = 33 · 54 · 77 · 174	Discriminant
Eigenvalues	1 3- 5- 7- -4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-56768,-4945867]	[a1,a2,a3,a4,a6]
Generators	[-141:580:1]	Generators of the group modulo torsion
j	171963096231529/9865918125	j-invariant
L	6.7988840795631	L(r)(E,1)/r!
Ω	0.31040379671013	Real period
R	0.91263972815708	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	37485x3 62475i3 1785b4	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12495p3

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	-	4	4	10	-4	-10	-6	4	-8	-6	-12	14	-12	8	-10	16	-12	2	-2

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Quadratic twists for elliptic curve 12495p3

-3	5	-7
37485x3	62475i3	1785b4

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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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