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	730k	Isogeny class
Conductor	730	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	73000 = 23 · 53 · 73	Discriminant
Eigenvalues	2-  1 5-  5  3 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-15,17]	[a1,a2,a3,a4,a6]
j	374805361/73000	j-invariant
L	3.2768778390811	L(r)(E,1)/r!
Ω	3.2768778390811	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5840l1 23360f1 6570g1 3650b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 730k1

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	-	5	3	-4	-6	-4	6	-9	2	-7	9	2	9	-12	9	-4	-7	-3	-	-1	12	-15	2

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Quadratic twists for elliptic curve 730k1

-4	8	-3	5	-7	-11	13	73
5840l1	23360f1	6570g1	3650b1	35770t1	88330n1	123370b1	53290u1

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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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