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	730i	Isogeny class
Conductor	730	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	56	Modular degree for the optimal curve
Δ	46720 = 27 · 5 · 73	Discriminant
Eigenvalues	2- -1 5+ -1 -1 -2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-26,39]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	1948441249/46720	j-invariant
L	2.5255155328271	L(r)(E,1)/r!
Ω	3.578150669783	Real period
R	0.10083083876479	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	5840d1 23360j1 6570k1 3650a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 730i1

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	+	-1	-1	-2	-2	-6	0	-1	-4	-9	-3	12	-5	0	-7	8	7	5	-	-5	-2	-11	12

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Quadratic twists for elliptic curve 730i1

-4	8	-3	5	-7	-11	13	73
5840d1	23360j1	6570k1	3650a1	35770ba1	88330e1	123370h1	53290y1

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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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