Cremona's table of elliptic curves

1575 = 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	3+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	1575d	Isogeny class
Conductor	1575	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-165375 = -1 · 33 · 53 · 72	Discriminant
Eigenvalues	-1 3+ 5- 7-  0 -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,10,12]	[a1,a2,a3,a4,a6]
Generators	[0:3:1]	Generators of the group modulo torsion
j	35937/49	j-invariant
L	1.8778075022872	L(r)(E,1)/r!
Ω	2.1773766856982	Real period
R	0.43120869131678	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200df1 100800ch1 1575c1 1575a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1575d1

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	0	0	8	-4	-8	4	-8	12	-6	8	10	-8	-16	-12	-8	-16	-12	-4

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Quadratic twists for elliptic curve 1575d1

-4	8	-3	5	-7
25200df1	100800ch1	1575c1	1575a1	11025o1

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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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