Cremona's table of elliptic curves

4025 = 5² · 7 · 23

Field	Data	Notes
Atkin-Lehner	5+ 7+ 23-	Signs for the Atkin-Lehner involutions
Class	4025a	Isogeny class
Conductor	4025	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-30607609375 = -1 · 56 · 7 · 234	Discriminant
Eigenvalues	1  0 5+ 7+  4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,658,5191]	[a1,a2,a3,a4,a6]
j	2014698447/1958887	j-invariant
L	1.5434849664318	L(r)(E,1)/r!
Ω	0.77174248321588	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	64400bo3 36225bf3 161a4 28175i3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4025a4

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

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Quadratic twists for elliptic curve 4025a4

-4	-3	5	-7	-23
64400bo3	36225bf3	161a4	28175i3	92575q3

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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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