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	15330r	Isogeny class
Conductor	15330	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	301797117193320 = 23 · 316 · 5 · 74 · 73	Discriminant
Eigenvalues	2- 3+ 5+ 7-  4 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-22271,-977731]	[a1,a2,a3,a4,a6]
Generators	[-107:494:1]	Generators of the group modulo torsion
j	1221642363806767729/301797117193320	j-invariant
L	6.0242610794705	L(r)(E,1)/r!
Ω	0.397870192251	Real period
R	2.5235454497473	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	122640cb3 45990bb3 76650bd3 107310ds3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 15330r3

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	-6	-2	0	0	-6	0	6	2	8	0	6	-4	-14	-12	0	+	8	-12	-14	-2

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Quadratic twists for elliptic curve 15330r3

-4	-3	5	-7
122640cb3	45990bb3	76650bd3	107310ds3

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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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