Cremona's table of elliptic curves

6256 = 2⁴ · 17 · 23

Field	Data	Notes
Atkin-Lehner	2+ 17+ 23+	Signs for the Atkin-Lehner involutions
Class	6256a	Isogeny class
Conductor	6256	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5248	Modular degree for the optimal curve
Δ	9208832 = 210 · 17 · 232	Discriminant
Eigenvalues	2+  2 -4  4 -2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3000,64256]	[a1,a2,a3,a4,a6]
Generators	[-4:276:1]	Generators of the group modulo torsion
j	2916972108004/8993	j-invariant
L	4.8565843418986	L(r)(E,1)/r!
Ω	2.0119863541354	Real period
R	1.2069128431007	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	3128a1 25024k1 56304q1 106352f1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 6256a1

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	-4	4	-2	2	+	0	+	0	-4	-8	-2	-4	-8	-2	-8	0	4	-8	10	16	12	10	-2

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Quadratic twists for elliptic curve 6256a1

-4	8	-3	17
3128a1	25024k1	56304q1	106352f1

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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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