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	5775b	Isogeny class
Conductor	5775	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	1403325 = 36 · 52 · 7 · 11	Discriminant
Eigenvalues	0 3+ 5+ 7+ 11+ -5 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-43,108]	[a1,a2,a3,a4,a6]
Generators	[-2:13:1]	Generators of the group modulo torsion
j	359956480/56133	j-invariant
L	2.3756344329735	L(r)(E,1)/r!
Ω	2.5845406438244	Real period
R	0.45958542742399	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	92400hn1 17325o1 5775y1 40425ce1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775b1

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
0	+	+	+	+	-5	-3	5	0	6	-4	7	3	4	12	-9	6	-1	-5	-15	-11	-10	0	12	16

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Quadratic twists for elliptic curve 5775b1

-4	-3	5	-7	-11
92400hn1	17325o1	5775y1	40425ce1	63525o1

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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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