Cremona's table of elliptic curves

730 = 2 · 5 · 73

Field	Data	Notes
Atkin-Lehner	2+ 5- 73+	Signs for the Atkin-Lehner involutions
Class	730d	Isogeny class
Conductor	730	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	648	Modular degree for the optimal curve
Δ	48989470720 = 227 · 5 · 73	Discriminant
Eigenvalues	2+ -1 5-  3  3  0  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1897,29189]	[a1,a2,a3,a4,a6]
j	755585074684441/48989470720	j-invariant
L	1.1089286592422	L(r)(E,1)/r!
Ω	1.1089286592422	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5840i1 23360a1 6570t1 3650o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 730d1

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	-	3	3	0	6	-4	-2	-1	-2	-1	1	6	7	12	9	0	7	5	+	-1	16	1	-14

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Quadratic twists for elliptic curve 730d1

-4	8	-3	5	-7	-11	13	73
5840i1	23360a1	6570t1	3650o1	35770g1	88330bk1	123370s1	53290e1

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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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