Cremona's table of elliptic curves

8645 = 5 · 7 · 13 · 19

Field	Data	Notes
Atkin-Lehner	5- 7- 13- 19-	Signs for the Atkin-Lehner involutions
Class	8645b	Isogeny class
Conductor	8645	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1632	Modular degree for the optimal curve
Δ	-40570985 = -1 · 5 · 7 · 132 · 193	Discriminant
Eigenvalues	-1 -1 5- 7- -2 13-  5 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,85,90]	[a1,a2,a3,a4,a6]
Generators	[0:9:1]	Generators of the group modulo torsion
j	67867385039/40570985	j-invariant
L	2.340471398826	L(r)(E,1)/r!
Ω	1.2474928581351	Real period
R	0.31269001976823	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	77805r1 43225a1 60515e1 112385a1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 8645b1

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
-1	-1	-	-	-2	-	5	-	3	-8	-4	-5	-3	-1	6	1	6	-10	4	-15	13	0	0	-6	10

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Quadratic twists for elliptic curve 8645b1

-3	5	-7	13
77805r1	43225a1	60515e1	112385a1

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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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