Cremona's table of elliptic curves

9610 = 2 · 5 · 31²

Field	Data	Notes
Atkin-Lehner	2- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	9610b	Isogeny class
Conductor	9610	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	170578207488200 = 23 · 52 · 318	Discriminant
Eigenvalues	2- -2 5+  0 -2  0 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1024446,399014140]	[a1,a2,a3,a4,a6]
Generators	[514:2626:1]	Generators of the group modulo torsion
j	133974081659809/192200	j-invariant
L	4.0493027736141	L(r)(E,1)/r!
Ω	0.48632419569582	Real period
R	1.3877240770157	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	76880p2 86490bb2 48050d2 310a2	Quadratic twists by: -4 -3 5 -31

Hecke Eigenvalues for elliptic curve 9610b2

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

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Quadratic twists for elliptic curve 9610b2

-4	-3	5	-31
76880p2	86490bb2	48050d2	310a2

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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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