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	730j	Isogeny class
Conductor	730	Conductor
∏ cp	63	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	2920000000 = 29 · 57 · 73	Discriminant
Eigenvalues	2- -1 5- -3 -3 -6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-405,-1925]	[a1,a2,a3,a4,a6]
Generators	[-7:28:1]	Generators of the group modulo torsion
j	7347774183121/2920000000	j-invariant
L	2.6051012064754	L(r)(E,1)/r!
Ω	1.1012771596479	Real period
R	0.037548052675875	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	5840h1 23360b1 6570d1 3650c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 730j1

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	-6	-6	2	4	5	4	-1	-11	-12	1	0	3	-12	7	5	+	11	10	13	-8

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Quadratic twists for elliptic curve 730j1

-4	8	-3	5	-7	-11	13	73
5840h1	23360b1	6570d1	3650c1	35770x1	88330p1	123370f1	53290w1

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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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