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	2	Product of Tamagawa factors cp
Δ	148000000 = 28 · 56 · 37	Discriminant
Eigenvalues	2-  1 5+ -1 -3 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12021,-511321]	[a1,a2,a3,a4,a6]
Generators	[-13746:125:216]	Generators of the group modulo torsion
j	750484394082304/578125	j-invariant
L	2.3309157286086	L(r)(E,1)/r!
Ω	0.45594390536716	Real period
R	2.5561430925714	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	2960i2 11840j2 6660e2 3700b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 740b2

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 740b2

-4	8	-3	5	-7	-11	13	37
2960i2	11840j2	6660e2	3700b2	36260p2	89540g2	125060e2	27380c2

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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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