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
Δ	94616222006250000 = 24 · 38 · 58 · 74 · 312	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-172190,23108555]	[a1,a2,a3,a4,a6]
j	564608806599700366561/94616222006250000	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	52080bz2 19530m2 32550t2 45570da2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510r2

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 6510r2

-4	-3	5	-7
52080bz2	19530m2	32550t2	45570da2

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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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