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	8415g	Isogeny class
Conductor	8415	Conductor
∏ cp	120	Product of Tamagawa factors cp
Δ	179647100768334375 = 39 · 55 · 112 · 176	Discriminant
Eigenvalues	1 3+ 5-  0 11+ -4 17-  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-480399,126647018]	[a1,a2,a3,a4,a6]
Generators	[-358:16074:1]	Generators of the group modulo torsion
j	622929950501217507/9127018278125	j-invariant
L	5.2377886267849	L(r)(E,1)/r!
Ω	0.32122341183087	Real period
R	0.54352499785443	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	8415d2 42075c2 92565n2	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 8415g2

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	+	-	0	+	-4	-	2	4	0	-2	4	8	4	6	-14	-8	2	-4	8	2	-4	-16	-8	-8

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Quadratic twists for elliptic curve 8415g2

-3	5	-11
8415d2	42075c2	92565n2

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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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