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
deg	12	Modular degree for the optimal curve
Δ	1872 = 24 · 32 · 13	Discriminant
Eigenvalues	2- 3+ -4 -2 -4 13-  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5,6]	[a1,a2,a3,a4,a6]
Generators	[-1:3:1]	Generators of the group modulo torsion
j	1048576/117	j-invariant
L	1.003503055032	L(r)(E,1)/r!
Ω	4.5382403755029	Real period
R	0.14741441204816	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	624j1 2496l1 468e1 3900h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 156a1

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 156a1

-4	8	-3	5	-7	-11	13	17	-19	-23
624j1	2496l1	468e1	3900h1	7644g1	18876d1	2028c1	45084p1	56316k1	82524e1

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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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