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	10400r	Isogeny class
Conductor	10400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-169000000000 = -1 · 29 · 59 · 132	Discriminant
Eigenvalues	2+ -2 5-  0  0 13+  4  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,792,18088]	[a1,a2,a3,a4,a6]
j	54872/169	j-invariant
L	1.4368974115412	L(r)(E,1)/r!
Ω	0.71844870577062	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	10400bd2 20800ca2 93600er2 10400bj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400r2

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	-	0	0	+	4	8	4	6	-2	2	2	-2	8	-10	12	10	-4	10	-10	-8	-12	6	-14

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Quadratic twists for elliptic curve 10400r2

-4	8	-3	5
10400bd2	20800ca2	93600er2	10400bj2

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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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