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	6510b	Isogeny class
Conductor	6510	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	678081600 = 26 · 32 · 52 · 72 · 312	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4 -6  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-273,-1323]	[a1,a2,a3,a4,a6]
Generators	[-13:22:1] [-9:27:1]	Generators of the group modulo torsion
j	2263054145689/678081600	j-invariant
L	3.2555669849444	L(r)(E,1)/r!
Ω	1.2011429387968	Real period
R	1.3551954891421	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	52080bt2 19530cd2 32550cn2 45570bj2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510b2

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

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Quadratic twists for elliptic curve 6510b2

-4	-3	5	-7
52080bt2	19530cd2	32550cn2	45570bj2

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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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