Cremona's table of elliptic curves

1675 = 5² · 67

Field	Data	Notes
Atkin-Lehner	5+ 67+	Signs for the Atkin-Lehner involutions
Class	1675a	Isogeny class
Conductor	1675	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-26171875 = -1 · 58 · 67	Discriminant
Eigenvalues	0  0 5+  2 -2  2  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-50,281]	[a1,a2,a3,a4,a6]
Generators	[5:12:1]	Generators of the group modulo torsion
j	-884736/1675	j-invariant
L	2.483886162462	L(r)(E,1)/r!
Ω	1.8870063897562	Real period
R	0.65815520709045	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26800w1 107200l1 15075c1 335a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1675a1

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	0	+	2	-2	2	3	-1	1	-9	0	3	-2	-6	-9	-12	5	0	+	-4	1	-4	4	3	14

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Quadratic twists for elliptic curve 1675a1

-4	8	-3	5	-7	-67
26800w1	107200l1	15075c1	335a1	82075a1	112225d1

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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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