Cremona's table of elliptic curves

5985 = 3² · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	5985m	Isogeny class
Conductor	5985	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-156434155567792515 = -1 · 36 · 5 · 7 · 1910	Discriminant
Eigenvalues	2 3- 5+ 7-  3 -1 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-149943,29352109]	[a1,a2,a3,a4,a6]
Generators	[-16961869418:-3061252528593:523606616]	Generators of the group modulo torsion
j	-511416541770305536/214587319023035	j-invariant
L	7.4034997047861	L(r)(E,1)/r!
Ω	0.30374891633903	Real period
R	12.186874267763	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	95760di2 665d2 29925s2 41895by2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5985m2

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

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Quadratic twists for elliptic curve 5985m2

-4	-3	5	-7	-19
95760di2	665d2	29925s2	41895by2	113715z2

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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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