Cremona's table of elliptic curves

7975 = 5² · 11 · 29

Field	Data	Notes
Atkin-Lehner	5+ 11- 29+	Signs for the Atkin-Lehner involutions
Class	7975c	Isogeny class
Conductor	7975	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	7950078125 = 57 · 112 · 292	Discriminant
Eigenvalues	1  2 5+  2 11-  4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-500,-625]	[a1,a2,a3,a4,a6]
j	887503681/508805	j-invariant
L	4.3809938504313	L(r)(E,1)/r!
Ω	1.0952484626078	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	127600u2 71775z2 1595c2 87725p2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 7975c2

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	2	+	2	-	4	-2	4	4	+	4	-8	2	-4	2	6	12	2	4	0	10	8	6	-10	4

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Quadratic twists for elliptic curve 7975c2

-4	-3	5	-11
127600u2	71775z2	1595c2	87725p2

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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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