Cremona's table of elliptic curves

363 = 3 · 11²

Field	Data	Notes
Atkin-Lehner	3+ 11-	Signs for the Atkin-Lehner involutions
Class	363b	Isogeny class
Conductor	363	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	-3267 = -1 · 33 · 112	Discriminant
Eigenvalues	2 3+  4 -1 11-  2 -4  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,4,-1]	[a1,a2,a3,a4,a6]
j	45056/27	j-invariant
L	2.7390143163183	L(r)(E,1)/r!
Ω	2.7390143163183	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5808bh1 23232cm1 1089k1 9075o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 363b1

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	+	4	-1	-	2	-4	3	2	-6	-5	3	2	-12	2	6	-10	-3	-1	0	11	-11	-6	12	5

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Quadratic twists for elliptic curve 363b1

-4	8	-3	5	-7	-11	13	17
5808bh1	23232cm1	1089k1	9075o1	17787bb1	363c1	61347u1	104907bg1

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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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