Cremona's table of elliptic curves

9270 = 2 · 3² · 5 · 103

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 103-	Signs for the Atkin-Lehner involutions
Class	9270d	Isogeny class
Conductor	9270	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-54316406250 = -1 · 2 · 33 · 510 · 103	Discriminant
Eigenvalues	2+ 3+ 5-  0  1 -4 -2  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1974,-35082]	[a1,a2,a3,a4,a6]
Generators	[57:159:1]	Generators of the group modulo torsion
j	-31515568179003/2011718750	j-invariant
L	3.4688509087303	L(r)(E,1)/r!
Ω	0.3567980985558	Real period
R	0.48610837932868	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74160z1 9270p1 46350bj1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 9270d1

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	1	-4	-2	7	1	1	-1	-9	8	-12	-6	-6	4	8	0	-6	0	-4	0	15	13

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Quadratic twists for elliptic curve 9270d1

-4	-3	5
74160z1	9270p1	46350bj1

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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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