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	10400w	Isogeny class
Conductor	10400	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	120960	Modular degree for the optimal curve
Δ	2509940680000000000 = 212 · 510 · 137	Discriminant
Eigenvalues	2- -1 5+  2 -2 13-  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-978333,364902037]	[a1,a2,a3,a4,a6]
Generators	[331:8788:1]	Generators of the group modulo torsion
j	2588953638400/62748517	j-invariant
L	3.7533360358909	L(r)(E,1)/r!
Ω	0.25670048139078	Real period
R	1.0443900598961	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	10400h1 20800e1 93600bo1 10400p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400w1

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
-	-1	+	2	-2	-	2	-2	1	-3	-4	10	-2	3	-6	-11	14	11	-10	0	-2	3	-6	12	-10

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Quadratic twists for elliptic curve 10400w1

-4	8	-3	5
10400h1	20800e1	93600bo1	10400p1

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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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