Cremona's table of elliptic curves

10400 = 2⁵ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 13+	Signs for the Atkin-Lehner involutions
Class	10400be	Isogeny class
Conductor	10400	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	20800000000 = 212 · 58 · 13	Discriminant
Eigenvalues	2- -3 5- -2 -2 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1000,10000]	[a1,a2,a3,a4,a6]
Generators	[0:100:1]	Generators of the group modulo torsion
j	69120/13	j-invariant
L	2.0801530744253	L(r)(E,1)/r!
Ω	1.1522659301459	Real period
R	0.30087861664622	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10400s1 20800cc1 93600cd1 10400m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400be1

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	-	-2	-2	+	-2	2	-5	5	0	2	2	1	-6	3	2	3	2	-8	10	7	2	-8	-18

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Quadratic twists for elliptic curve 10400be1

-4	8	-3	5
10400s1	20800cc1	93600cd1	10400m1

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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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