Cremona's table of elliptic curves

75 = 3 · 5²

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Class	75c	Isogeny class
Conductor	75	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-29296875 = -1 · 3 · 510	Discriminant
Eigenvalues	-2 3- 5+  3  2 -1 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-208,-1256]	[a1,a2,a3,a4,a6]
j	-102400/3	j-invariant
L	0.62723492949639	L(r)(E,1)/r!
Ω	0.62723492949639	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	1200k2 4800e2 225d2 75a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 75c2

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 75c2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200k2	4800e2	225d2	75a1	3675f2	9075n2	12675bb2	21675i2	27075i2	39675bi2	63075d2	72075m2	102675t2	126075l2

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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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