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	10400o	Isogeny class
Conductor	10400	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	308915776000 = 29 · 53 · 136	Discriminant
Eigenvalues	2+  0 5-  0 -6 13+ -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3715,-82950]	[a1,a2,a3,a4,a6]
j	88597239912/4826809	j-invariant
L	0.61359405626344	L(r)(E,1)/r!
Ω	0.61359405626344	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10400n2 20800dx2 93600es2 10400bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400o2

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	-	0	-6	+	-4	-6	6	-2	0	6	2	-12	12	-10	-6	10	-12	-12	-2	0	12	-10	10

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Quadratic twists for elliptic curve 10400o2

-4	8	-3	5
10400n2	20800dx2	93600es2	10400bg2

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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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