Cremona's table of elliptic curves

740 = 2² · 5 · 37

Field	Data	Notes
Atkin-Lehner	2- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	740b	Isogeny class
Conductor	740	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	324179200 = 28 · 52 · 373	Discriminant
Eigenvalues	2-  1 5+ -1 -3 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-181,-425]	[a1,a2,a3,a4,a6]
Generators	[-3:10:1]	Generators of the group modulo torsion
j	2575826944/1266325	j-invariant
L	2.3309157286086	L(r)(E,1)/r!
Ω	1.3678317161015	Real period
R	0.8520476975238	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2960i1 11840j1 6660e1 3700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 740b1

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	+	-1	-3	-4	0	-4	0	0	2	-	3	2	3	-9	0	2	-4	15	-7	-10	-3	6	-10

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Quadratic twists for elliptic curve 740b1

-4	8	-3	5	-7	-11	13	37
2960i1	11840j1	6660e1	3700b1	36260p1	89540g1	125060e1	27380c1

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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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