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	8	Product of Tamagawa factors cp
Δ	3515625 = 32 · 58	Discriminant
Eigenvalues	1 3- 5+  0 -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-126,523]	[a1,a2,a3,a4,a6]
j	13997521/225	j-invariant
L	1.2527374448595	L(r)(E,1)/r!
Ω	2.505474889719	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	1200j2 4800b2 225c2 15a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 75b2

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 75b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200j2	4800b2	225c2	15a3	3675e2	9075l2	12675x2	21675c2	27075g2	39675bc2	63075c2	72075f2	102675s2	126075c2

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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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