Cremona's table of elliptic curves

9594 = 2 · 3² · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 41+	Signs for the Atkin-Lehner involutions
Class	9594a	Isogeny class
Conductor	9594	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	89856	Modular degree for the optimal curve
Δ	118983048900378624 = 226 · 39 · 133 · 41	Discriminant
Eigenvalues	2+ 3+  1  2  1 13+ -5  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-202434,30930452]	[a1,a2,a3,a4,a6]
Generators	[42020:89582:125]	Generators of the group modulo torsion
j	46610525182518387/6044965142528	j-invariant
L	3.7705149659708	L(r)(E,1)/r!
Ω	0.31954421004505	Real period
R	2.9499165118962	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	76752x1 9594k1 124722bd1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 9594a1

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	1	+	-5	0	7	3	1	-10	+	-12	1	-1	-4	1	-2	8	4	1	-6	-2	-15

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Quadratic twists for elliptic curve 9594a1

-4	-3	13
76752x1	9594k1	124722bd1

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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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