Cremona's table of elliptic curves

13545 = 3² · 5 · 7 · 43

Field	Data	Notes
Atkin-Lehner	3+ 5- 7- 43-	Signs for the Atkin-Lehner involutions
Class	13545d	Isogeny class
Conductor	13545	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-2996628075 = -1 · 33 · 52 · 74 · 432	Discriminant
Eigenvalues	-1 3+ 5- 7- -6 -6 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,268,-2086]	[a1,a2,a3,a4,a6]
Generators	[7:6:1] [12:46:1]	Generators of the group modulo torsion
j	79119341757/110986225	j-invariant
L	4.5679980626639	L(r)(E,1)/r!
Ω	0.75738897531232	Real period
R	0.75390555770553	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13545b2 67725b2 94815d2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 13545d2

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
-1	+	-	-	-6	-6	-4	-4	-2	-6	-8	-6	8	-	-6	0	-10	-10	4	-12	-14	-8	-10	10	2

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Quadratic twists for elliptic curve 13545d2

-3	5	-7
13545b2	67725b2	94815d2

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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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