Cremona's table of elliptic curves

30056 = 2³ · 13 · 17²

Field	Data	Notes
Atkin-Lehner	2- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	30056k	Isogeny class
Conductor	30056	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	1021904 = 24 · 13 · 173	Discriminant
Eigenvalues	2- -2 -2 -4 -4 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-79,-294]	[a1,a2,a3,a4,a6]
Generators	[-5:1:1] [10:4:1]	Generators of the group modulo torsion
j	702464/13	j-invariant
L	4.4449665678236	L(r)(E,1)/r!
Ω	1.6014877110204	Real period
R	2.7755233694503	Regulator
r	2	Rank of the group of rational points
S	0.99999999999981	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	60112f1 30056h1	Quadratic twists by: -4 17

Hecke Eigenvalues for elliptic curve 30056k1

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

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Quadratic twists for elliptic curve 30056k1

-4	17
60112f1	30056h1

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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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