Cremona's table of elliptic curves

23865 = 3 · 5 · 37 · 43

Field	Data	Notes
Atkin-Lehner	3+ 5- 37+ 43+	Signs for the Atkin-Lehner involutions
Class	23865b	Isogeny class
Conductor	23865	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	15040	Modular degree for the optimal curve
Δ	-44746875 = -1 · 32 · 55 · 37 · 43	Discriminant
Eigenvalues	-2 3+ 5- -1  0 -5 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-650,6608]	[a1,a2,a3,a4,a6]
Generators	[14:7:1] [-16:112:1]	Generators of the group modulo torsion
j	-30418077085696/44746875	j-invariant
L	3.6618018983179	L(r)(E,1)/r!
Ω	2.0206608640091	Real period
R	0.18121803433416	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	71595a1 119325p1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 23865b1

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
-2	+	-	-1	0	-5	-3	-7	-3	2	-8	+	-3	+	12	0	-10	9	-4	-6	3	10	-2	6	-18

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Quadratic twists for elliptic curve 23865b1

-3	5
71595a1	119325p1

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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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