Cremona's table of elliptic curves

20400 = 2⁴ · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 17-	Signs for the Atkin-Lehner involutions
Class	20400bq	Isogeny class
Conductor	20400	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	29952	Modular degree for the optimal curve
Δ	7163154000 = 24 · 36 · 53 · 173	Discriminant
Eigenvalues	2+ 3- 5-  4 -2  4 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8143,-285532]	[a1,a2,a3,a4,a6]
j	29860725364736/3581577	j-invariant
L	4.5231879766079	L(r)(E,1)/r!
Ω	0.50257644184532	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	10200n1 81600hp1 61200ci1 20400o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20400bq1

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
+	-	-	4	-2	4	-	4	8	8	0	-2	-4	-6	12	14	0	2	-2	-14	2	-4	16	-6	-14

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Quadratic twists for elliptic curve 20400bq1

-4	8	-3	5
10200n1	81600hp1	61200ci1	20400o1

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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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