Cremona's table of elliptic curves

1675 = 5² · 67

Field	Data	Notes
Atkin-Lehner	5+ 67+	Signs for the Atkin-Lehner involutions
Class	1675b	Isogeny class
Conductor	1675	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-1675 = -1 · 52 · 67	Discriminant
Eigenvalues	0  2 5+ -2  0  4 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-13,23]	[a1,a2,a3,a4,a6]
Generators	[3:1:1]	Generators of the group modulo torsion
j	-10485760/67	j-invariant
L	3.1572942985358	L(r)(E,1)/r!
Ω	4.7561176782696	Real period
R	0.66383855743545	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	26800bd1 107200x1 15075d1 1675d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1675b1

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 1675b1

-4	8	-3	5	-7	-67
26800bd1	107200x1	15075d1	1675d1	82075b1	112225e1

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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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