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	20400bx	Isogeny class
Conductor	20400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	-46473750000 = -1 · 24 · 37 · 57 · 17	Discriminant
Eigenvalues	2- 3+ 5+  3 -1  2 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,742,-7113]	[a1,a2,a3,a4,a6]
j	180472064/185895	j-invariant
L	2.4619448022801	L(r)(E,1)/r!
Ω	0.61548620057002	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	5100k1 81600ib1 61200fv1 4080bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20400bx1

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	-1	2	+	-1	6	7	10	3	-9	8	3	-5	-8	10	16	-12	9	-2	12	0	2

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Quadratic twists for elliptic curve 20400bx1

-4	8	-3	5
5100k1	81600ib1	61200fv1	4080bf1

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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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