Cremona's table of elliptic curves

40425 = 3 · 5² · 7² · 11

Field	Data	Notes
Atkin-Lehner	3- 5- 7- 11-	Signs for the Atkin-Lehner involutions
Class	40425df	Isogeny class
Conductor	40425	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-772472074623046875 = -1 · 34 · 59 · 79 · 112	Discriminant
Eigenvalues	-1 3- 5- 7- 11- -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,140237,37153892]	[a1,a2,a3,a4,a6]
Generators	[53:6662:1]	Generators of the group modulo torsion
j	3869893/9801	j-invariant
L	4.1021755029176	L(r)(E,1)/r!
Ω	0.19837877788114	Real period
R	2.584812465029	Regulator
r	1	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121275ft2 40425bn2 40425bp2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 40425df2

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	-	-	-	-	-6	2	-4	2	6	2	4	-6	4	0	8	-6	6	-10	8	-10	-4	0	-12	-14

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Quadratic twists for elliptic curve 40425df2

-3	5	-7
121275ft2	40425bn2	40425bp2

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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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