Cremona's table of elliptic curves

30400 = 2⁶ · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	30400bh	Isogeny class
Conductor	30400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	860160	Modular degree for the optimal curve
Δ	-1855468750000000000 = -1 · 210 · 520 · 19	Discriminant
Eigenvalues	2-  2 5+  4  4 -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2603533,1619131437]	[a1,a2,a3,a4,a6]
j	-121981271658244096/115966796875	j-invariant
L	4.721198997431	L(r)(E,1)/r!
Ω	0.26228883319074	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30400q1 7600f1 6080n1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 30400bh1

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	2	+	0	-2	-8	4	6	0	12	-8	0	-2	14	-8	-6	4	-4	14	12

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Quadratic twists for elliptic curve 30400bh1

-4	8	5
30400q1	7600f1	6080n1

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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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