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	5775k	Isogeny class
Conductor	5775	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	109634765625 = 36 · 59 · 7 · 11	Discriminant
Eigenvalues	1 3+ 5- 7+ 11-  0  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1325,9000]	[a1,a2,a3,a4,a6]
Generators	[-36:126:1]	Generators of the group modulo torsion
j	131872229/56133	j-invariant
L	3.8416979876581	L(r)(E,1)/r!
Ω	0.95333265747445	Real period
R	4.0297559907739	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	92400id1 17325bj1 5775z1 40425dc1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775k1

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

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Quadratic twists for elliptic curve 5775k1

-4	-3	5	-7	-11
92400id1	17325bj1	5775z1	40425dc1	63525be1

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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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