Cremona's table of elliptic curves

4056 = 2³ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	4056b	Isogeny class
Conductor	4056	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	-626481193728 = -1 · 28 · 3 · 138	Discriminant
Eigenvalues	2+ 3+ -2  1 -6 13+  8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2929,-70955]	[a1,a2,a3,a4,a6]
Generators	[113:1014:1]	Generators of the group modulo torsion
j	-13312/3	j-invariant
L	2.6566229808344	L(r)(E,1)/r!
Ω	0.32062611039781	Real period
R	0.69047791562638	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8112n1 32448bb1 12168p1 101400dc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056b1

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	1	-6	+	8	-4	2	10	7	2	-4	-7	6	0	-6	-5	-7	6	1	1	0	4	-19

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Quadratic twists for elliptic curve 4056b1

-4	8	-3	5	13
8112n1	32448bb1	12168p1	101400dc1	4056l1

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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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