Cremona's table of elliptic curves

42075 = 3² · 5² · 11 · 17

Field	Data	Notes
Atkin-Lehner	3+ 5- 11+ 17+	Signs for the Atkin-Lehner involutions
Class	42075o	Isogeny class
Conductor	42075	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	143360	Modular degree for the optimal curve
Δ	-532935755859375 = -1 · 33 · 59 · 112 · 174	Discriminant
Eigenvalues	-1 3+ 5-  0 11+  4 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-35180,-2763178]	[a1,a2,a3,a4,a6]
j	-91307371527/10106041	j-invariant
L	0.69287609240582	L(r)(E,1)/r!
Ω	0.17321902309676	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42075r1 42075p1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 42075o1

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

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Quadratic twists for elliptic curve 42075o1

-3	5
42075r1	42075p1

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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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