Cremona's table of elliptic curves

3135 = 3 · 5 · 11 · 19

Field	Data	Notes
Atkin-Lehner	3+ 5- 11- 19+	Signs for the Atkin-Lehner involutions
Class	3135b	Isogeny class
Conductor	3135	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	44983823445 = 316 · 5 · 11 · 19	Discriminant
Eigenvalues	-1 3+ 5-  0 11- -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5710,163382]	[a1,a2,a3,a4,a6]
Generators	[51:64:1]	Generators of the group modulo torsion
j	20589072861673441/44983823445	j-invariant
L	1.9523265426857	L(r)(E,1)/r!
Ω	1.1393041678651	Real period
R	3.4272261925348	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	50160ca4 9405e3 15675s4 34485h4	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3135b4

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

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Quadratic twists for elliptic curve 3135b4

-4	-3	5	-11	-19
50160ca4	9405e3	15675s4	34485h4	59565u4

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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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