Cremona's table of elliptic curves

2975 = 5² · 7 · 17

Field	Data	Notes
Atkin-Lehner	5+ 7+ 17-	Signs for the Atkin-Lehner involutions
Class	2975b	Isogeny class
Conductor	2975	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	23520	Modular degree for the optimal curve
Δ	-683605029296875 = -1 · 511 · 77 · 17	Discriminant
Eigenvalues	-2 -2 5+ 7+  6 -1 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,10842,-1176906]	[a1,a2,a3,a4,a6]
j	9019694698496/43750721875	j-invariant
L	0.5134254327736	L(r)(E,1)/r!
Ω	0.2567127163868	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	47600bc1 26775z1 595b1 20825m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2975b1

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	+	+	6	-1	-	-6	5	6	9	5	-9	0	1	6	-6	-7	-14	12	8	0	-15	-10	4

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Quadratic twists for elliptic curve 2975b1

-4	-3	5	-7	17
47600bc1	26775z1	595b1	20825m1	50575t1

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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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