Cremona's table of elliptic curves

814 = 2 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2- 11+ 37-	Signs for the Atkin-Lehner involutions
Class	814b	Isogeny class
Conductor	814	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-13024 = -1 · 25 · 11 · 37	Discriminant
Eigenvalues	2-  0 -1 -4 11+  4 -7 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-28,63]	[a1,a2,a3,a4,a6]
Generators	[3:-1:1]	Generators of the group modulo torsion
j	-2347334289/13024	j-invariant
L	2.848711036555	L(r)(E,1)/r!
Ω	4.0087531499415	Real period
R	0.1421245424701	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6512d1 26048c1 7326e1 20350b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 814b1

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
-	0	-1	-4	+	4	-7	-4	2	4	-6	-	-2	2	-11	0	4	10	8	3	12	-13	1	-16	-10

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Quadratic twists for elliptic curve 814b1

-4	8	-3	5	-7	-11	37
6512d1	26048c1	7326e1	20350b1	39886o1	8954c1	30118b1

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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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