Cremona's table of elliptic curves

1610 = 2 · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 23+	Signs for the Atkin-Lehner involutions
Class	1610f	Isogeny class
Conductor	1610	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	1610000 = 24 · 54 · 7 · 23	Discriminant
Eigenvalues	2-  0 5- 7+ -4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-37,-51]	[a1,a2,a3,a4,a6]
Generators	[9:12:1]	Generators of the group modulo torsion
j	5461074081/1610000	j-invariant
L	3.9000243575857	L(r)(E,1)/r!
Ω	1.9838239616445	Real period
R	1.9659125169315	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12880y1 51520c1 14490k1 8050l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1610f1

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

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Quadratic twists for elliptic curve 1610f1

-4	8	-3	5	-7	-23
12880y1	51520c1	14490k1	8050l1	11270k1	37030o1

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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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