Cremona's table of elliptic curves

42050 = 2 · 5² · 29²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 29+	Signs for the Atkin-Lehner involutions
Class	42050g	Isogeny class
Conductor	42050	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	105125000 = 23 · 56 · 292	Discriminant
Eigenvalues	2+ -2 5+  1  6  4 -3  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3701,-86952]	[a1,a2,a3,a4,a6]
Generators	[-2252:1169:64]	Generators of the group modulo torsion
j	426477625/8	j-invariant
L	3.3775124201422	L(r)(E,1)/r!
Ω	0.6121168435445	Real period
R	2.7588788445886	Regulator
r	1	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1682f2 42050bd2	Quadratic twists by: 5 29

Hecke Eigenvalues for elliptic curve 42050g2

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	+	1	6	4	-3	4	-9	+	-5	2	6	-4	-9	12	6	-2	-8	3	11	-11	0	-3	17

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Quadratic twists for elliptic curve 42050g2

5	29
1682f2	42050bd2

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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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