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	730g	Isogeny class
Conductor	730	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	730 = 2 · 5 · 73	Discriminant
Eigenvalues	2+ -3 5- -1 -3 -2  6  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4,-2]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	8120601/730	j-invariant
L	1.1443062568171	L(r)(E,1)/r!
Ω	3.3565977386937	Real period
R	0.34091253879663	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	5840m1 23360g1 6570v1 3650m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 730g1

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
+	-3	-	-1	-3	-2	6	6	-4	-3	4	-3	-3	-8	-13	8	-5	-8	-11	-3	-	11	-2	-11	8

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Quadratic twists for elliptic curve 730g1

-4	8	-3	5	-7	-11	13	73
5840m1	23360g1	6570v1	3650m1	35770f1	88330bh1	123370r1	53290j1

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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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