Cremona's table of elliptic curves

8415 = 3² · 5 · 11 · 17

Field	Data	Notes
Atkin-Lehner	3- 5- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	8415o	Isogeny class
Conductor	8415	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-212631929296875 = -1 · 37 · 58 · 114 · 17	Discriminant
Eigenvalues	-1 3- 5-  4 11+ -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11732,-852294]	[a1,a2,a3,a4,a6]
j	-244950111766009/291676171875	j-invariant
L	1.7548217639744	L(r)(E,1)/r!
Ω	0.2193527204968	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2805b4 42075x3 92565br3	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 8415o4

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

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Quadratic twists for elliptic curve 8415o4

-3	5	-11
2805b4	42075x3	92565br3

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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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