Cremona's table of elliptic curves

7973 = 7 · 17 · 67

Field	Data	Notes
Atkin-Lehner	7+ 17+ 67-	Signs for the Atkin-Lehner involutions
Class	7973d	Isogeny class
Conductor	7973	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	464	Modular degree for the optimal curve
Δ	7973 = 7 · 17 · 67	Discriminant
Eigenvalues	-2  0  0 7+ -3  1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-5,0]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1] [0:0:1]	Generators of the group modulo torsion
j	13824000/7973	j-invariant
L	2.9663675393021	L(r)(E,1)/r!
Ω	3.5346814640247	Real period
R	0.83921778227929	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	127568x1 71757k1 55811o1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 7973d1

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
-2	0	0	+	-3	1	+	-6	-4	-6	-4	-8	2	-4	-6	-10	10	-4	-	-8	11	-11	-16	8	-12

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Quadratic twists for elliptic curve 7973d1

-4	-3	-7
127568x1	71757k1	55811o1

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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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