Cremona's table of elliptic curves

12558 = 2 · 3 · 7 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 13+ 23-	Signs for the Atkin-Lehner involutions
Class	12558i	Isogeny class
Conductor	12558	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	5199989414256 = 24 · 39 · 74 · 13 · 232	Discriminant
Eigenvalues	2+ 3-  2 7+  2 13+  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-21834985,39269676476]	[a1,a2,a3,a4,a6]
Generators	[2692:-829:1]	Generators of the group modulo torsion
j	1151283756590458788537587593/5199989414256	j-invariant
L	4.8279192120287	L(r)(E,1)/r!
Ω	0.36715813272506	Real period
R	0.73052374466248	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	100464bf2 37674n2 87906i2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12558i2

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
+	-	2	+	2	+	0	4	-	-6	0	-4	2	-6	-12	-12	4	-6	-12	-16	-6	-10	-6	2	-8

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Quadratic twists for elliptic curve 12558i2

-4	-3	-7
100464bf2	37674n2	87906i2

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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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