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	50400df	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	20643840	Modular degree for the optimal curve
Δ	6.6739232675391E+22	Discriminant
Eigenvalues	2- 3- 5+ 7+  4  6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1435218825,-20927879219000]	[a1,a2,a3,a4,a6]
Generators	[-997404381748346328419845670780983461891643862503:-59952752374212476117888819000497628240783603232:45612246962293071156270010896556702536862777]	Generators of the group modulo torsion
j	448487713888272974160064/91549016015625	j-invariant
L	7.110675065061	L(r)(E,1)/r!
Ω	0.024528445724101	Real period
R	72.473763167086	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	50400dw1 100800mi2 16800r1 10080t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400df1

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	6	6	-4	-4	2	8	-6	-6	-8	0	6	4	10	-8	-12	14	-16	-12	-14	-18

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Quadratic twists for elliptic curve 50400df1

-4	8	-3	5
50400dw1	100800mi2	16800r1	10080t1

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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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