Cremona's table of elliptic curves

75 = 3 · 5²

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Class	75b	Isogeny class
Conductor	75	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	791015625 = 34 · 510	Discriminant
Eigenvalues	1 3- 5+  0 -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-251,-727]	[a1,a2,a3,a4,a6]
j	111284641/50625	j-invariant
L	1.2527374448595	L(r)(E,1)/r!
Ω	1.2527374448595	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1200j4 4800b3 225c4 15a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 75b3

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

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Quadratic twists for elliptic curve 75b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200j4	4800b3	225c4	15a1	3675e4	9075l4	12675x3	21675c3	27075g3	39675bc3	63075c3	72075f3	102675s3	126075c3

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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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