Cremona's table of elliptic curves

156 = 2² · 3 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	156b	Isogeny class
Conductor	156	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	316368 = 24 · 32 · 133	Discriminant
Eigenvalues	2- 3-  0  2  0 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-733,-7888]	[a1,a2,a3,a4,a6]
j	2725888000000/19773	j-invariant
L	1.3761495936397	L(r)(E,1)/r!
Ω	0.91743306242647	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	624g3 2496a3 468d3 3900c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 156b3

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
-	-	0	2	0	-	-6	2	0	-6	2	2	-12	-4	0	6	12	2	-10	12	14	8	12	0	-10

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Quadratic twists for elliptic curve 156b3

-4	8	-3	5	-7	-11	13	17	-19	-23
624g3	2496a3	468d3	3900c3	7644a3	18876h3	2028d3	45084g3	56316d3	82524j3

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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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