Cremona's table of elliptic curves

78400 = 2⁶ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	78400y	Isogeny class
Conductor	78400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	884736	Modular degree for the optimal curve
Δ	-1349292851200000000 = -1 · 222 · 58 · 77	Discriminant
Eigenvalues	2+  0 5+ 7- -4  6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,181300,47334000]	[a1,a2,a3,a4,a6]
j	1367631/2800	j-invariant
L	0.7493465443048	L(r)(E,1)/r!
Ω	0.18733663193319	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	78400gy1 2450e1 15680f1 11200p1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400y1

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	+	-	-4	6	2	0	0	-6	-8	-10	-2	4	8	-2	-8	-14	-12	-16	2	-8	-8	-10	2

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Quadratic twists for elliptic curve 78400y1

-4	8	5	-7
78400gy1	2450e1	15680f1	11200p1

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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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