Cremona's table of elliptic curves

1612 = 2² · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 13+ 31+	Signs for the Atkin-Lehner involutions
Class	1612a	Isogeny class
Conductor	1612	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2340	Modular degree for the optimal curve
Δ	-2831664579328 = -1 · 28 · 135 · 313	Discriminant
Eigenvalues	2-  0 -4 -2  1 13+  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-272,80980]	[a1,a2,a3,a4,a6]
j	-8693415936/11061189763	j-invariant
L	0.64908123901434	L(r)(E,1)/r!
Ω	0.64908123901434	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	6448e1 25792o1 14508g1 40300d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1612a1

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	-4	-2	1	+	0	0	-4	2	+	3	6	-8	4	12	14	-8	-2	10	11	-10	12	-9	8

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Quadratic twists for elliptic curve 1612a1

-4	8	-3	5	-7	13	-31
6448e1	25792o1	14508g1	40300d1	78988h1	20956e1	49972d1

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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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