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	730f	Isogeny class
Conductor	730	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	730000 = 24 · 54 · 73	Discriminant
Eigenvalues	2+  0 5-  2 -6 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-949,11493]	[a1,a2,a3,a4,a6]
Generators	[17:-1:1]	Generators of the group modulo torsion
j	94575738893481/730000	j-invariant
L	1.7537639411641	L(r)(E,1)/r!
Ω	2.5571125378521	Real period
R	0.34291880298652	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5840k1 23360e1 6570x1 3650i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 730f1

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
+	0	-	2	-6	-2	-6	0	-4	6	-2	-6	6	10	-10	-10	-2	10	-8	0	-	-4	-2	10	-10

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Quadratic twists for elliptic curve 730f1

-4	8	-3	5	-7	-11	13	73
5840k1	23360e1	6570x1	3650i1	35770c1	88330bf1	123370l1	53290d1

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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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