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	32	Product of Tamagawa factors cp
Δ	2562890625 = 38 · 58	Discriminant
Eigenvalues	1 3- 5+  0 -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3376,-75727]	[a1,a2,a3,a4,a6]
j	272223782641/164025	j-invariant
L	1.2527374448595	L(r)(E,1)/r!
Ω	0.62636872242974	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	1200j5 4800b5 225c5 15a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 75b5

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 75b5

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200j5	4800b5	225c5	15a2	3675e5	9075l5	12675x5	21675c6	27075g6	39675bc6	63075c6	72075f6	102675s6	126075c6

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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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