Cremona's table of elliptic curves

42834 = 2 · 3 · 11² · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 59-	Signs for the Atkin-Lehner involutions
Class	42834bc	Isogeny class
Conductor	42834	Conductor
∏ cp	216	Product of Tamagawa factors cp
deg	145152	Modular degree for the optimal curve
Δ	15007125602304 = 218 · 36 · 113 · 59	Discriminant
Eigenvalues	2- 3- -2 -4 11+ -2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-11734,451364]	[a1,a2,a3,a4,a6]
Generators	[-124:122:1] [-100:842:1]	Generators of the group modulo torsion
j	134241322342427/11275075584	j-invariant
L	12.838344856864	L(r)(E,1)/r!
Ω	0.68395464161991	Real period
R	0.34760656995597	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	128502i1 42834m1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 42834bc1

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

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Quadratic twists for elliptic curve 42834bc1

-3	-11
128502i1	42834m1

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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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