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	12400v	Isogeny class
Conductor	12400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	-50384076800 = -1 · 221 · 52 · 312	Discriminant
Eigenvalues	2- -1 5+  0  1  0  1  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-488,-11408]	[a1,a2,a3,a4,a6]
Generators	[36:128:1]	Generators of the group modulo torsion
j	-125768785/492032	j-invariant
L	3.7491494315438	L(r)(E,1)/r!
Ω	0.46385060367771	Real period
R	1.0103332306291	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	1550b1 49600cd1 111600eq1 12400bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400v1

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	+	0	1	0	1	7	-4	-4	-	-4	-3	-4	6	-2	4	-6	-5	6	3	10	-15	9	-10

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Quadratic twists for elliptic curve 12400v1

-4	8	-3	5
1550b1	49600cd1	111600eq1	12400bc1

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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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