Cremona's table of elliptic curves

50400 = 2⁵ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	50400bl	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	2152828125000000 = 26 · 39 · 512 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7- -2  4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-47325,-3274000]	[a1,a2,a3,a4,a6]
Generators	[361:5166:1]	Generators of the group modulo torsion
j	16079333824/2953125	j-invariant
L	6.2050419223098	L(r)(E,1)/r!
Ω	0.32778757494535	Real period
R	4.7325176399207	Regulator
r	1	Rank of the group of rational points
S	1.0000000000011	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400w1 100800ng2 16800bh1 10080bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400bl1

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

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Quadratic twists for elliptic curve 50400bl1

-4	8	-3	5
50400w1	100800ng2	16800bh1	10080bl1

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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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