Cremona's table of elliptic curves

1209 = 3 · 13 · 31

Field	Data	Notes
Atkin-Lehner	3+ 13- 31+	Signs for the Atkin-Lehner involutions
Class	1209a	Isogeny class
Conductor	1209	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-22868673867 = -1 · 310 · 13 · 313	Discriminant
Eigenvalues	-2 3+  2  2  1 13-  8  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-442,-7962]	[a1,a2,a3,a4,a6]
j	-9571339399168/22868673867	j-invariant
L	0.97143908999855	L(r)(E,1)/r!
Ω	0.48571954499927	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	19344t1 77376o1 3627b1 30225v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1209a1

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	+	2	2	1	-	8	6	6	-4	+	-5	6	-6	0	-12	-6	-2	-8	12	11	8	4	13	-14

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Quadratic twists for elliptic curve 1209a1

-4	8	-3	5	-7	13	-31
19344t1	77376o1	3627b1	30225v1	59241v1	15717a1	37479e1

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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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