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	12400s	Isogeny class
Conductor	12400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	750781250000 = 24 · 511 · 312	Discriminant
Eigenvalues	2-  0 5+ -2  4  4  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26300,-1641125]	[a1,a2,a3,a4,a6]
Generators	[766545:12361250:2197]	Generators of the group modulo torsion
j	8047314026496/3003125	j-invariant
L	4.412006036702	L(r)(E,1)/r!
Ω	0.37490423311117	Real period
R	5.8841774072391	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3100a1 49600bz1 111600fd1 2480n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400s1

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
-	0	+	-2	4	4	0	0	-4	2	-	-8	6	-8	-6	8	-4	2	-2	0	4	0	-8	6	2

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Quadratic twists for elliptic curve 12400s1

-4	8	-3	5
3100a1	49600bz1	111600fd1	2480n1

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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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