Cremona's table of elliptic curves

4485 = 3 · 5 · 13 · 23

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+ 23+	Signs for the Atkin-Lehner involutions
Class	4485a	Isogeny class
Conductor	4485	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3200	Modular degree for the optimal curve
Δ	-5738086575 = -1 · 310 · 52 · 132 · 23	Discriminant
Eigenvalues	-1 3+ 5+  4  2 13+  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1041,-13866]	[a1,a2,a3,a4,a6]
Generators	[89:735:1]	Generators of the group modulo torsion
j	-124767644120209/5738086575	j-invariant
L	2.1766278113035	L(r)(E,1)/r!
Ω	0.41912130976654	Real period
R	2.5966561000155	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	71760br1 13455l1 22425r1 58305f1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4485a1

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	+	+	4	2	+	0	0	+	-6	0	-8	-10	2	8	-8	12	-14	0	-12	2	10	-6	2	16

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Quadratic twists for elliptic curve 4485a1

-4	-3	5	13	-23
71760br1	13455l1	22425r1	58305f1	103155e1

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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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