Cremona's table of elliptic curves

6975 = 3² · 5² · 31

Field	Data	Notes
Atkin-Lehner	3- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	6975m	Isogeny class
Conductor	6975	Conductor
∏ cp	10	Product of Tamagawa factors cp
Δ	-1630519615546875 = -1 · 36 · 57 · 315	Discriminant
Eigenvalues	-2 3- 5+  2 -2  6 -7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-189075,31704156]	[a1,a2,a3,a4,a6]
Generators	[240:387:1]	Generators of the group modulo torsion
j	-65626385453056/143145755	j-invariant
L	2.246557097889	L(r)(E,1)/r!
Ω	0.47499632176459	Real period
R	0.47296305149124	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	111600dy2 775c2 1395c2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6975m2

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	-	+	2	-2	6	-7	-5	4	0	-	7	3	-9	-2	9	5	-8	-8	3	1	0	-11	-10	-18

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Quadratic twists for elliptic curve 6975m2

-4	-3	5
111600dy2	775c2	1395c2

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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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