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	128	Product of Tamagawa factors cp
Δ	75097045898437500 = 22 · 34 · 516 · 72 · 31	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2632970,1643286107]	[a1,a2,a3,a4,a6]
j	2018651992700195476824481/75097045898437500	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	4	Number of elements in the torsion subgroup
Twists	52080bz4 19530m3 32550t4 45570da4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510r4

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 6510r4

-4	-3	5	-7
52080bz4	19530m3	32550t4	45570da4

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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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