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	5775a	Isogeny class
Conductor	5775	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-7958671875 = -1 · 33 · 57 · 73 · 11	Discriminant
Eigenvalues	0 3+ 5+ 7+ 11+  4 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-33,-4282]	[a1,a2,a3,a4,a6]
Generators	[32:162:1]	Generators of the group modulo torsion
j	-262144/509355	j-invariant
L	2.5566106409634	L(r)(E,1)/r!
Ω	0.59465134471038	Real period
R	2.1496719579509	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	92400hl1 17325m1 1155j1 40425cc1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775a1

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	+	+	+	+	4	-3	-1	3	-9	-10	4	6	1	6	9	15	-13	-2	-6	16	8	3	-9	-17

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Quadratic twists for elliptic curve 5775a1

-4	-3	5	-7	-11
92400hl1	17325m1	1155j1	40425cc1	63525m1

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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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