Cremona's table of elliptic curves

13530 = 2 · 3 · 5 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 11- 41-	Signs for the Atkin-Lehner involutions
Class	13530s	Isogeny class
Conductor	13530	Conductor
∏ cp	384	Product of Tamagawa factors cp
deg	86016	Modular degree for the optimal curve
Δ	642945600000000 = 212 · 34 · 58 · 112 · 41	Discriminant
Eigenvalues	2- 3+ 5- -4 11-  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-21705,153975]	[a1,a2,a3,a4,a6]
Generators	[-107:1178:1]	Generators of the group modulo torsion
j	1130848257596386321/642945600000000	j-invariant
L	5.6588269396341	L(r)(E,1)/r!
Ω	0.44017543141422	Real period
R	0.53566019134813	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	108240cf1 40590l1 67650bk1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13530s1

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	-6	-4	0	2	8	-2	-	12	4	-6	4	-2	-12	-12	10	12	12	-6	-14

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Quadratic twists for elliptic curve 13530s1

-4	-3	5
108240cf1	40590l1	67650bk1

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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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