Cremona's table of elliptic curves

1815 = 3 · 5 · 11²

Field	Data	Notes
Atkin-Lehner	3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	1815b	Isogeny class
Conductor	1815	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	99825 = 3 · 52 · 113	Discriminant
Eigenvalues	1 3- 5+  2 11+ -4  6  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-14,-13]	[a1,a2,a3,a4,a6]
j	205379/75	j-invariant
L	2.5658301426449	L(r)(E,1)/r!
Ω	2.5658301426449	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	29040bv1 116160bh1 5445j1 9075d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1815b1

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	6	6	4	-6	8	-6	6	6	8	6	0	-4	12	8	-16	-2	0	10	-6

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Quadratic twists for elliptic curve 1815b1

-4	8	-3	5	-7	-11
29040bv1	116160bh1	5445j1	9075d1	88935ba1	1815c1

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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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