Cremona's table of elliptic curves

13325 = 5² · 13 · 41

Field	Data	Notes
Atkin-Lehner	5+ 13- 41-	Signs for the Atkin-Lehner involutions
Class	13325d	Isogeny class
Conductor	13325	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	267264	Modular degree for the optimal curve
Δ	71091607666015625 = 514 · 132 · 413	Discriminant
Eigenvalues	1  2 5+ -2  2 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6061275,-5746243000]	[a1,a2,a3,a4,a6]
Generators	[790340310480:-113643603952115:37933056]	Generators of the group modulo torsion
j	1576143528848064470449/4549862890625	j-invariant
L	7.5386025429794	L(r)(E,1)/r!
Ω	0.096218509148568	Real period
R	13.058129545774	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	119925be1 2665c1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 13325d1

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	2	+	-2	2	-	-2	6	0	2	-4	-10	-	8	2	-2	0	-10	10	-6	-6	6	-8	2	-10

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Quadratic twists for elliptic curve 13325d1

-3	5
119925be1	2665c1

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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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