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	12495q	Isogeny class
Conductor	12495	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	725447125930078125 = 33 · 58 · 77 · 174	Discriminant
Eigenvalues	-1 3- 5- 7-  0  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-233780,14595027]	[a1,a2,a3,a4,a6]
Generators	[529:-6512:1]	Generators of the group modulo torsion
j	12010404962647729/6166198828125	j-invariant
L	3.9676956020635	L(r)(E,1)/r!
Ω	0.25149990677514	Real period
R	0.32866940629483	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	37485r3 62475f3 1785c4	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12495q3

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

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Quadratic twists for elliptic curve 12495q3

-3	5	-7
37485r3	62475f3	1785c4

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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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