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	4025d	Isogeny class
Conductor	4025	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-14175546875 = -1 · 57 · 73 · 232	Discriminant
Eigenvalues	-2 -3 5+ 7- -1 -7 -3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-325,6156]	[a1,a2,a3,a4,a6]
Generators	[-24:11:1] [20:-88:1]	Generators of the group modulo torsion
j	-242970624/907235	j-invariant
L	1.7000900122303	L(r)(E,1)/r!
Ω	1.0944558414978	Real period
R	0.064723565042243	Regulator
r	2	Rank of the group of rational points
S	0.99999999999828	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	64400bm1 36225by1 805d1 28175h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4025d1

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	-3	+	-	-1	-7	-3	-8	+	-5	-2	4	-8	-6	-3	-2	2	-14	4	8	6	-3	-12	-2	-7

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Quadratic twists for elliptic curve 4025d1

-4	-3	5	-7	-23
64400bm1	36225by1	805d1	28175h1	92575m1

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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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