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	12400h	Isogeny class
Conductor	12400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	30031250000 = 24 · 59 · 312	Discriminant
Eigenvalues	2+  2 5+ -4 -4 -4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-783,1562]	[a1,a2,a3,a4,a6]
j	212629504/120125	j-invariant
L	1.0132428178781	L(r)(E,1)/r!
Ω	1.0132428178781	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6200c1 49600ck1 111600bu1 2480d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400h1

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
+	2	+	-4	-4	-4	-4	-4	2	2	-	-8	-6	10	0	0	-4	2	8	16	0	16	18	6	10

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Quadratic twists for elliptic curve 12400h1

-4	8	-3	5
6200c1	49600ck1	111600bu1	2480d1

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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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