Cremona's table of elliptic curves

6510 = 2 · 3 · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 31+	Signs for the Atkin-Lehner involutions
Class	6510r	Isogeny class
Conductor	6510	Conductor
∏ cp	512	Product of Tamagawa factors cp
deg	40960	Modular degree for the optimal curve
Δ	-2316066449760000 = -1 · 28 · 34 · 54 · 78 · 31	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,19890,2056587]	[a1,a2,a3,a4,a6]
j	870215264126076959/2316066449760000	j-invariant
L	2.5814882231805	L(r)(E,1)/r!
Ω	0.32268602789757	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	52080bz1 19530m1 32550t1 45570da1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510r1

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

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Quadratic twists for elliptic curve 6510r1

-4	-3	5	-7
52080bz1	19530m1	32550t1	45570da1

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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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