Cremona's table of elliptic curves

2805 = 3 · 5 · 11 · 17

Field	Data	Notes
Atkin-Lehner	3+ 5+ 11+ 17-	Signs for the Atkin-Lehner involutions
Class	2805a	Isogeny class
Conductor	2805	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	620143425 = 33 · 52 · 11 · 174	Discriminant
Eigenvalues	-1 3+ 5+  0 11+  6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-251,848]	[a1,a2,a3,a4,a6]
j	1749254553649/620143425	j-invariant
L	0.7452913181207	L(r)(E,1)/r!
Ω	1.4905826362414	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	44880co1 8415q1 14025p1 30855c1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2805a1

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

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Quadratic twists for elliptic curve 2805a1

-4	-3	5	-11	17
44880co1	8415q1	14025p1	30855c1	47685q1

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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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