Cremona's table of elliptic curves

5740 = 2² · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 41-	Signs for the Atkin-Lehner involutions
Class	5740a	Isogeny class
Conductor	5740	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	6589520 = 24 · 5 · 72 · 412	Discriminant
Eigenvalues	2-  0 5+ 7+  4  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-68,177]	[a1,a2,a3,a4,a6]
Generators	[2:7:1]	Generators of the group modulo torsion
j	2173353984/411845	j-invariant
L	3.6019109307979	L(r)(E,1)/r!
Ω	2.254312847238	Real period
R	0.53259554387213	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22960l1 91840p1 51660m1 28700c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5740a1

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	4	0	-4	-6	2	4	-2	-	-2	-8	4	0	-2	4	8	-14	-8	6	2	12

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Quadratic twists for elliptic curve 5740a1

-4	8	-3	5	-7
22960l1	91840p1	51660m1	28700c1	40180f1

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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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