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	6510s	Isogeny class
Conductor	6510	Conductor
∏ cp	315	Product of Tamagawa factors cp
deg	211680	Modular degree for the optimal curve
Δ	-216436381560000000 = -1 · 29 · 33 · 57 · 7 · 315	Discriminant
Eigenvalues	2- 3+ 5- 7- -6 -7  7  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-824600,288736985]	[a1,a2,a3,a4,a6]
Generators	[-517:24283:1]	Generators of the group modulo torsion
j	-62008858471273416662401/216436381560000000	j-invariant
L	5.2671263539014	L(r)(E,1)/r!
Ω	0.31683789131672	Real period
R	0.052774735921394	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	52080bx1 19530s1 32550u1 45570ct1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510s1

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
-	+	-	-	-6	-7	7	1	2	-4	-	-2	7	-2	2	1	4	-12	-3	-12	-14	10	-18	2	-5

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Quadratic twists for elliptic curve 6510s1

-4	-3	5	-7
52080bx1	19530s1	32550u1	45570ct1

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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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