Cremona's table of elliptic curves

12400 = 2⁴ · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 31+	Signs for the Atkin-Lehner involutions
Class	12400n	Isogeny class
Conductor	12400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	-6200000000000 = -1 · 212 · 511 · 31	Discriminant
Eigenvalues	2- -1 5+ -2 -2  6  7  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3867,-77363]	[a1,a2,a3,a4,a6]
j	99897344/96875	j-invariant
L	1.6454355254092	L(r)(E,1)/r!
Ω	0.4113588813523	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	775c1 49600bp1 111600dy1 2480m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400n1

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	6	7	5	4	0	+	7	-3	9	-2	-9	5	-8	8	3	1	0	-11	10	-18

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Quadratic twists for elliptic curve 12400n1

-4	8	-3	5
775c1	49600bp1	111600dy1	2480m1

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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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