Cremona's table of elliptic curves

5610 = 2 · 3 · 5 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 11- 17+	Signs for the Atkin-Lehner involutions
Class	5610n	Isogeny class
Conductor	5610	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	1038579300 = 22 · 33 · 52 · 113 · 172	Discriminant
Eigenvalues	2+ 3- 5+  2 11- -4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-18729,984952]	[a1,a2,a3,a4,a6]
Generators	[-74:1439:1]	Generators of the group modulo torsion
j	726497538898787209/1038579300	j-invariant
L	3.4461483901171	L(r)(E,1)/r!
Ω	1.3228093811851	Real period
R	1.3025869180901	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	44880bc1 16830cp1 28050cj1 61710co1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 5610n1

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	-	-4	+	2	-6	6	-4	-10	6	-10	0	12	6	-10	8	-6	-16	-10	-12	6	-10

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Quadratic twists for elliptic curve 5610n1

-4	-3	5	-11	17
44880bc1	16830cp1	28050cj1	61710co1	95370p1

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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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