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	10400l	Isogeny class
Conductor	10400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-270400000000 = -1 · 212 · 58 · 132	Discriminant
Eigenvalues	2+ -2 5+ -4  6 13-  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2033,-43937]	[a1,a2,a3,a4,a6]
j	-14526784/4225	j-invariant
L	1.4008816422189	L(r)(E,1)/r!
Ω	0.35022041055474	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	10400k2 20800co1 93600eq2 2080c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400l2

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

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Quadratic twists for elliptic curve 10400l2

-4	8	-3	5
10400k2	20800co1	93600eq2	2080c2

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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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