Cremona's table of elliptic curves

36414 = 2 · 3² · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	36414bb	Isogeny class
Conductor	36414	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	235008	Modular degree for the optimal curve
Δ	-5980344757199064 = -1 · 23 · 37 · 72 · 178	Discriminant
Eigenvalues	2+ 3- -1 7+  3  0 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-236745,44552389]	[a1,a2,a3,a4,a6]
Generators	[-361:9284:1]	Generators of the group modulo torsion
j	-288568081/1176	j-invariant
L	3.6306412527868	L(r)(E,1)/r!
Ω	0.4275047374294	Real period
R	0.70771949698531	Regulator
r	1	Rank of the group of rational points
S	0.99999999999956	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12138r1 36414bg1	Quadratic twists by: -3 17

Hecke Eigenvalues for elliptic curve 36414bb1

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	+	3	0	-	0	-4	3	-5	4	0	6	-12	7	-7	-6	6	12	3	-5	8	16	-7

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Quadratic twists for elliptic curve 36414bb1

-3	17
12138r1	36414bg1

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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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