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	12400k	Isogeny class
Conductor	12400	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	-372387500000000 = -1 · 28 · 511 · 313	Discriminant
Eigenvalues	2+  3 5+  2  2  2  1 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-961300,362775500]	[a1,a2,a3,a4,a6]
j	-24560689104608256/93096875	j-invariant
L	5.6465251853577	L(r)(E,1)/r!
Ω	0.47054376544647	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	6200j1 49600cm1 111600bl1 2480g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400k1

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
+	3	+	2	2	2	1	-1	4	4	-	-3	-3	-11	-2	-3	7	4	8	-3	15	12	17	-6	2

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Quadratic twists for elliptic curve 12400k1

-4	8	-3	5
6200j1	49600cm1	111600bl1	2480g1

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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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