Cremona's table of elliptic curves

15330 = 2 · 3 · 5 · 7 · 73

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+ 73-	Signs for the Atkin-Lehner involutions
Class	15330h	Isogeny class
Conductor	15330	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	83490828540000 = 25 · 3 · 54 · 72 · 734	Discriminant
Eigenvalues	2+ 3- 5+ 7+ -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-27864,1733062]	[a1,a2,a3,a4,a6]
Generators	[274:3695:1]	Generators of the group modulo torsion
j	2392388417155129849/83490828540000	j-invariant
L	3.4530427121602	L(r)(E,1)/r!
Ω	0.60331278991094	Real period
R	1.4308675242364	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	122640bg3 45990cg3 76650by3 107310z3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 15330h4

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
+	-	+	+	-4	-2	2	-4	0	2	-4	10	2	-4	0	10	4	14	4	16	-	-8	-8	2	10

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Quadratic twists for elliptic curve 15330h4

-4	-3	5	-7
122640bg3	45990cg3	76650by3	107310z3

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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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