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	20400cy	Isogeny class
Conductor	20400	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	110160000000000 = 213 · 34 · 510 · 17	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-74408,7771188]	[a1,a2,a3,a4,a6]
Generators	[-212:3750:1]	Generators of the group modulo torsion
j	711882749089/1721250	j-invariant
L	5.9712733746825	L(r)(E,1)/r!
Ω	0.59498131423394	Real period
R	1.2545085937637	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	2550a3 81600ff4 61200fg4 4080t4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20400cy4

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
-	-	+	0	-4	-2	+	4	4	2	4	6	-10	-8	0	-6	8	10	-8	-8	2	-4	4	-14	10

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Quadratic twists for elliptic curve 20400cy4

-4	8	-3	5
2550a3	81600ff4	61200fg4	4080t4

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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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