Cremona's table of elliptic curves

775 = 5² · 31

Field	Data	Notes
Atkin-Lehner	5+ 31-	Signs for the Atkin-Lehner involutions
Class	775b	Isogeny class
Conductor	775	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-12109375 = -1 · 58 · 31	Discriminant
Eigenvalues	1 -2 5+ -4  4  0  8  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-26,-177]	[a1,a2,a3,a4,a6]
j	-117649/775	j-invariant
L	0.94547187184516	L(r)(E,1)/r!
Ω	0.94547187184516	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	12400o1 49600y1 6975k1 155b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 775b1

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	+	-4	4	0	8	4	-2	-6	-	4	-6	6	-8	12	-4	10	-8	0	4	0	-2	14	18

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Quadratic twists for elliptic curve 775b1

-4	8	-3	5	-7	-11	-31
12400o1	49600y1	6975k1	155b1	37975a1	93775g1	24025d1

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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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