Cremona's table of elliptic curves

75 = 3 · 5²

Field	Data	Notes
Atkin-Lehner	3+ 5-	Signs for the Atkin-Lehner involutions
Class	75a	Isogeny class
Conductor	75	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	6	Modular degree for the optimal curve
Δ	-1875 = -1 · 3 · 54	Discriminant
Eigenvalues	2 3+ 5- -3  2  1  2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-8,-7]	[a1,a2,a3,a4,a6]
j	-102400/3	j-invariant
L	1.4025399402162	L(r)(E,1)/r!
Ω	1.4025399402162	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1200r1 4800bf1 225e1 75c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 75a1

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	2	1	2	-5	6	10	-3	2	-8	1	2	-4	-10	7	-3	-8	-14	0	6	0	17

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Quadratic twists for elliptic curve 75a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200r1	4800bf1	225e1	75c2	3675q1	9075j1	12675s1	21675z1	27075w1	39675w1	63075v1	72075bo1	102675o1	126075be1

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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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