Cremona's table of elliptic curves

5775 = 3 · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	5775n	Isogeny class
Conductor	5775	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	40854515625 = 32 · 56 · 74 · 112	Discriminant
Eigenvalues	1 3- 5+ 7+ 11+ -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-976,6473]	[a1,a2,a3,a4,a6]
j	6570725617/2614689	j-invariant
L	2.0832599646327	L(r)(E,1)/r!
Ω	1.0416299823163	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	92400ev2 17325u2 231a2 40425k2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775n2

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	-	+	+	+	-6	-2	4	0	-2	8	-6	10	4	8	-6	4	-10	12	0	-2	16	-4	18	-2

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Quadratic twists for elliptic curve 5775n2

-4	-3	5	-7	-11
92400ev2	17325u2	231a2	40425k2	63525bv2

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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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