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	1612d	Isogeny class
Conductor	1612	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-14166256 = -1 · 24 · 134 · 31	Discriminant
Eigenvalues	2-  2  1  3  2 13-  6  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-70,-267]	[a1,a2,a3,a4,a6]
j	-2404846336/885391	j-invariant
L	3.2375990423095	L(r)(E,1)/r!
Ω	0.80939976057738	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	6448k1 25792m1 14508k1 40300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1612d1

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	1	3	2	-	6	3	-6	-8	-	-6	11	0	0	12	-7	-2	-4	-3	6	4	6	-12	-3

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Quadratic twists for elliptic curve 1612d1

-4	8	-3	5	-7	13	-31
6448k1	25792m1	14508k1	40300c1	78988e1	20956b1	49972b1

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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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