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	156a	Isogeny class
Conductor	156	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	129792 = 28 · 3 · 132	Discriminant
Eigenvalues	2- 3+ -4 -2 -4 13-  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-20,-24]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	3631696/507	j-invariant
L	1.003503055032	L(r)(E,1)/r!
Ω	2.2691201877515	Real period
R	0.29482882409632	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	624j2 2496l2 468e2 3900h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 156a2

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
-	+	-4	-2	-4	-	2	-2	0	-6	-10	10	8	4	-4	-10	-8	-14	2	16	-10	-16	0	-4	-2

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Quadratic twists for elliptic curve 156a2

-4	8	-3	5	-7	-11	13	17	-19	-23
624j2	2496l2	468e2	3900h2	7644g2	18876d2	2028c2	45084p2	56316k2	82524e2

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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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