Cremona's table of elliptic curves

1608 = 2³ · 3 · 67

Field	Data	Notes
Atkin-Lehner	2+ 3+ 67-	Signs for the Atkin-Lehner involutions
Class	1608a	Isogeny class
Conductor	1608	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	416	Modular degree for the optimal curve
Δ	-154368 = -1 · 28 · 32 · 67	Discriminant
Eigenvalues	2+ 3+ -4 -4 -6 -4 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-25,61]	[a1,a2,a3,a4,a6]
Generators	[19:-78:1] [-3:10:1]	Generators of the group modulo torsion
j	-7023616/603	j-invariant
L	2.3303612858807	L(r)(E,1)/r!
Ω	3.1760326056854	Real period
R	0.091716678290307	Regulator
r	2	Rank of the group of rational points
S	0.99999999999968	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3216b1 12864q1 4824d1 40200bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1608a1

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
+	+	-4	-4	-6	-4	-3	-7	5	1	4	7	-12	-6	-13	-2	-11	-6	-	0	9	4	4	-3	-8

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Quadratic twists for elliptic curve 1608a1

-4	8	-3	5	-7	-67
3216b1	12864q1	4824d1	40200bg1	78792o1	107736e1

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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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