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	5775c	Isogeny class
Conductor	5775	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	60310457328515625 = 312 · 58 · 74 · 112	Discriminant
Eigenvalues	1 3+ 5+ 7+ 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-299250,-62015625]	[a1,a2,a3,a4,a6]
Generators	[12302100:5387446575:64]	Generators of the group modulo torsion
j	189674274234120481/3859869269025	j-invariant
L	3.7730231749349	L(r)(E,1)/r!
Ω	0.20437513897374	Real period
R	9.2306314600712	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	92400hd2 17325s2 1155m2 40425cg2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775c2

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	+	+	+	+	2	-2	4	0	6	0	-6	-6	4	0	2	4	6	-12	0	-10	8	4	10	-10

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Quadratic twists for elliptic curve 5775c2

-4	-3	5	-7	-11
92400hd2	17325s2	1155m2	40425cg2	63525r2

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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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