Cremona's table of elliptic curves

1675 = 5² · 67

Field	Data	Notes
Atkin-Lehner	5- 67-	Signs for the Atkin-Lehner involutions
Class	1675d	Isogeny class
Conductor	1675	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	420	Modular degree for the optimal curve
Δ	-26171875 = -1 · 58 · 67	Discriminant
Eigenvalues	0 -2 5-  2  0 -4  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-333,2244]	[a1,a2,a3,a4,a6]
Generators	[4:31:1]	Generators of the group modulo torsion
j	-10485760/67	j-invariant
L	1.7973384762628	L(r)(E,1)/r!
Ω	2.1270004875199	Real period
R	2.535032530752	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	26800bk1 107200be1 15075n1 1675b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1675d1

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	-2	-	2	0	-4	3	-4	9	3	-4	2	0	-10	0	12	-9	-10	-	-3	5	14	-15	-18	-4

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Quadratic twists for elliptic curve 1675d1

-4	8	-3	5	-7	-67
26800bk1	107200be1	15075n1	1675b1	82075k1	112225i1

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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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