Cremona's table of elliptic curves

363 = 3 · 11²

Field	Data	Notes
Atkin-Lehner	3+ 11-	Signs for the Atkin-Lehner involutions
Class	363a	Isogeny class
Conductor	363	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	526153617 = 33 · 117	Discriminant
Eigenvalues	-1 3+ -2 -4 11-  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-789,8130]	[a1,a2,a3,a4,a6]
j	30664297/297	j-invariant
L	0.41376904699126	L(r)(E,1)/r!
Ω	1.655076187965	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	5808bg1 23232ca1 1089g1 9075k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 363a1

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

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Quadratic twists for elliptic curve 363a1

-4	8	-3	5	-7	-11	13	17
5808bg1	23232ca1	1089g1	9075k1	17787u1	33a2	61347j1	104907bf1

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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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