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	730h	Isogeny class
Conductor	730	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	140	Modular degree for the optimal curve
Δ	-456250 = -1 · 2 · 55 · 73	Discriminant
Eigenvalues	2- -2 5+  4  0 -4  7  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,19,-5]	[a1,a2,a3,a4,a6]
j	756058031/456250	j-invariant
L	1.7236786394383	L(r)(E,1)/r!
Ω	1.7236786394383	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	5840b1 23360h1 6570j1 3650d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 730h1

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
-	-2	+	4	0	-4	7	1	1	3	9	-1	9	-11	0	6	2	8	-2	-8	+	-4	-4	9	-16

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Quadratic twists for elliptic curve 730h1

-4	8	-3	5	-7	-11	13	73
5840b1	23360h1	6570j1	3650d1	35770bf1	88330i1	123370k1	53290ba1

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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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