Cremona's table of elliptic curves

12325 = 5² · 17 · 29

Field	Data	Notes
Atkin-Lehner	5+ 17+ 29+	Signs for the Atkin-Lehner involutions
Class	12325c	Isogeny class
Conductor	12325	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-94941015625 = -1 · 58 · 172 · 292	Discriminant
Eigenvalues	1  2 5+  0 -4  6 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1150,20625]	[a1,a2,a3,a4,a6]
Generators	[24:75:1]	Generators of the group modulo torsion
j	-10779215329/6076225	j-invariant
L	7.6048762531775	L(r)(E,1)/r!
Ω	0.99175241305699	Real period
R	1.9170299343503	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	110925bk2 2465a2	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 12325c2

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	2	+	0	-4	6	+	-2	4	+	-4	6	-6	8	0	6	-4	-2	6	-6	6	-4	-6	-14	-10

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Quadratic twists for elliptic curve 12325c2

-3	5
110925bk2	2465a2

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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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