Cremona's table of elliptic curves

7300 = 2² · 5² · 73

Field	Data	Notes
Atkin-Lehner	2- 5+ 73-	Signs for the Atkin-Lehner involutions
Class	7300d	Isogeny class
Conductor	7300	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	29200 = 24 · 52 · 73	Discriminant
Eigenvalues	2- -1 5+ -4  0  4 -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-18,-23]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	1703680/73	j-invariant
L	2.8315611465453	L(r)(E,1)/r!
Ω	2.3133284954096	Real period
R	0.40800678217037	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	29200u1 116800o1 65700j1 7300e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7300d1

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
-	-1	+	-4	0	4	-4	1	8	-6	0	7	-6	2	-6	6	-4	2	8	-5	-	5	10	3	13

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Quadratic twists for elliptic curve 7300d1

-4	8	-3	5
29200u1	116800o1	65700j1	7300e1

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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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