Cremona's table of elliptic curves

3255 = 3 · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	3+ 5- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	3255d	Isogeny class
Conductor	3255	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	824727341025 = 36 · 52 · 72 · 314	Discriminant
Eigenvalues	-1 3+ 5- 7+  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-18925,993242]	[a1,a2,a3,a4,a6]
Generators	[202:2236:1]	Generators of the group modulo torsion
j	749605580278405201/824727341025	j-invariant
L	1.9473486085038	L(r)(E,1)/r!
Ω	0.88882778118118	Real period
R	4.3818356035541	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	52080cf2 9765e2 16275t2 22785o2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3255d2

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
-1	+	-	+	4	-2	-6	4	-8	6	-	-2	-6	-4	8	6	-12	6	-12	0	10	8	12	-6	2

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Quadratic twists for elliptic curve 3255d2

-4	-3	5	-7	-31
52080cf2	9765e2	16275t2	22785o2	100905s2

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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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