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	5775l	Isogeny class
Conductor	5775	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	52800	Modular degree for the optimal curve
Δ	57072448125 = 34 · 54 · 7 · 115	Discriminant
Eigenvalues	2 3+ 5- 7+ 11-  1 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-869758,-311919507]	[a1,a2,a3,a4,a6]
Generators	[-1476538:-1273:2744]	Generators of the group modulo torsion
j	116423188793017446400/91315917	j-invariant
L	6.3569366397614	L(r)(E,1)/r!
Ω	0.15633272753142	Real period
R	4.0662865288292	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	92400ie1 17325bl1 5775v2 40425dg1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775l1

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	+	-	+	-	1	-3	5	-4	0	2	-3	-3	-4	-8	11	0	-13	-3	7	-9	-10	-4	10	-8

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Quadratic twists for elliptic curve 5775l1

-4	-3	5	-7	-11
92400ie1	17325bl1	5775v2	40425dg1	63525bf1

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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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