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
Δ	-117485546875 = -1 · 58 · 673	Discriminant
Eigenvalues	0 -2 5-  2  0 -4  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,917,12869]	[a1,a2,a3,a4,a6]
Generators	[-3:100:1]	Generators of the group modulo torsion
j	218071040/300763	j-invariant
L	1.7973384762628	L(r)(E,1)/r!
Ω	0.70900016250663	Real period
R	0.845010843584	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	26800bk2 107200be2 15075n2 1675b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1675d2

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 1675d2

-4	8	-3	5	-7	-67
26800bk2	107200be2	15075n2	1675b2	82075k2	112225i2

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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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