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	740a	Isogeny class
Conductor	740	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	12480	Modular degree for the optimal curve
Δ	6934395700000000 = 28 · 58 · 375	Discriminant
Eigenvalues	2-  3 5+ -3  5  2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-219448,39364772]	[a1,a2,a3,a4,a6]
j	4565397831743545344/27087483203125	j-invariant
L	2.5349965954153	L(r)(E,1)/r!
Ω	0.42249943256921	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2960h1 11840v1 6660c1 3700e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 740a1

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
-	3	+	-3	5	2	4	-4	6	6	-4	+	-9	10	-11	-11	-8	-8	-8	3	7	8	-9	-16	12

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Quadratic twists for elliptic curve 740a1

-4	8	-3	5	-7	-11	13	37
2960h1	11840v1	6660c1	3700e1	36260n1	89540f1	125060j1	27380e1

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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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