Cremona's table of elliptic curves

5325 = 3 · 5² · 71

Field	Data	Notes
Atkin-Lehner	3+ 5- 71-	Signs for the Atkin-Lehner involutions
Class	5325d	Isogeny class
Conductor	5325	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	47520	Modular degree for the optimal curve
Δ	-38758594921875 = -1 · 39 · 58 · 712	Discriminant
Eigenvalues	0 3+ 5- -5 -2 -1  4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-562333,-162120432]	[a1,a2,a3,a4,a6]
Generators	[6096204:555117715:729]	Generators of the group modulo torsion
j	-50343703509729280/99222003	j-invariant
L	1.9779145805322	L(r)(E,1)/r!
Ω	0.087170803813326	Real period
R	11.34505186374	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	85200du1 15975p1 5325l1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 5325d1

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	+	-	-5	-2	-1	4	-1	6	-8	-5	2	0	9	8	8	-12	9	-5	-	6	8	-4	0	-9

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Quadratic twists for elliptic curve 5325d1

-4	-3	5
85200du1	15975p1	5325l1

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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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