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	5775f	Isogeny class
Conductor	5775	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	144000	Modular degree for the optimal curve
Δ	-265426681201171875 = -1 · 35 · 511 · 75 · 113	Discriminant
Eigenvalues	2 3+ 5+ 7+ 11-  6  7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-223508,47704043]	[a1,a2,a3,a4,a6]
j	-79028701534867456/16987307596875	j-invariant
L	3.5599345501617	L(r)(E,1)/r!
Ω	0.29666121251348	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	92400gz1 17325k1 1155n1 40425cs1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775f1

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	+	+	+	-	6	7	-5	1	-5	-8	2	12	11	-8	11	-5	7	2	12	-4	-10	1	15	-3

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Quadratic twists for elliptic curve 5775f1

-4	-3	5	-7	-11
92400gz1	17325k1	1155n1	40425cs1	63525v1

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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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