Cremona's table of elliptic curves

13524 = 2² · 3 · 7² · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 23-	Signs for the Atkin-Lehner involutions
Class	13524d	Isogeny class
Conductor	13524	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	169344	Modular degree for the optimal curve
Δ	-903201005776349952 = -1 · 28 · 37 · 78 · 234	Discriminant
Eigenvalues	2- 3+  2 7+  2  5 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-377757,100509417]	[a1,a2,a3,a4,a6]
Generators	[523:6762:1]	Generators of the group modulo torsion
j	-4039597907968/612012267	j-invariant
L	4.8938105277814	L(r)(E,1)/r!
Ω	0.2704565639181	Real period
R	0.50262851586189	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	54096cg1 40572m1 13524k1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13524d1

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
-	+	2	+	2	5	-4	-5	-	0	3	-5	2	-1	-2	-12	0	2	-7	-10	-11	1	6	-12	-14

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Quadratic twists for elliptic curve 13524d1

-4	-3	-7
54096cg1	40572m1	13524k1

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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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