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	50400q	Isogeny class
Conductor	50400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	1512000 = 26 · 33 · 53 · 7	Discriminant
Eigenvalues	2+ 3+ 5- 7- -2  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-45,-100]	[a1,a2,a3,a4,a6]
Generators	[-4:4:1]	Generators of the group modulo torsion
j	46656/7	j-invariant
L	6.1763906269256	L(r)(E,1)/r!
Ω	1.8618356340745	Real period
R	1.6586831065667	Regulator
r	1	Rank of the group of rational points
S	1.0000000000063	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400cp1 100800cm1 50400cs1 50400cq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400q1

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

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Quadratic twists for elliptic curve 50400q1

-4	8	-3	5
50400cp1	100800cm1	50400cs1	50400cq1

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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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