Cremona's table of elliptic curves

12369 = 3 · 7 · 19 · 31

Field	Data	Notes
Atkin-Lehner	3- 7- 19+ 31+	Signs for the Atkin-Lehner involutions
Class	12369i	Isogeny class
Conductor	12369	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	1290576302127 = 312 · 7 · 192 · 312	Discriminant
Eigenvalues	1 3- -2 7-  6  0  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13007,-569401]	[a1,a2,a3,a4,a6]
Generators	[-69:61:1]	Generators of the group modulo torsion
j	243336431492632297/1290576302127	j-invariant
L	6.2881422584392	L(r)(E,1)/r!
Ω	0.44719602757325	Real period
R	1.1717721593224	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	37107l2 86583o2	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 12369i2

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

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Quadratic twists for elliptic curve 12369i2

-3	-7
37107l2	86583o2

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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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