Cremona's table of elliptic curves

35739 = 3² · 11 · 19²

Field	Data	Notes
Atkin-Lehner	3+ 11+ 19+	Signs for the Atkin-Lehner involutions
Class	35739c	Isogeny class
Conductor	35739	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-127560705745923153 = -1 · 33 · 114 · 199	Discriminant
Eigenvalues	1 3+  0 -4 11+ -4 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,57873,-16341246]	[a1,a2,a3,a4,a6]
Generators	[58304916:-2119018357:46656]	Generators of the group modulo torsion
j	2460375/14641	j-invariant
L	3.9678927671241	L(r)(E,1)/r!
Ω	0.16499137973114	Real period
R	12.024545687144	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	35739i2 35739d2	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 35739c2

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

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Quadratic twists for elliptic curve 35739c2

-3	-19
35739i2	35739d2

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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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