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	1612c	Isogeny class
Conductor	1612	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-83824 = -1 · 24 · 132 · 31	Discriminant
Eigenvalues	2- -2  3 -3  2 13-  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,6,-11]	[a1,a2,a3,a4,a6]
Generators	[5:13:1]	Generators of the group modulo torsion
j	1257728/5239	j-invariant
L	2.3121327254106	L(r)(E,1)/r!
Ω	1.7281994131358	Real period
R	0.66894268908911	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	6448m1 25792e1 14508h1 40300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1612c1

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	3	-3	2	-	0	-7	-4	6	+	-8	5	-10	8	-10	7	-8	-4	-5	-2	4	-6	-2	-17

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Quadratic twists for elliptic curve 1612c1

-4	8	-3	5	-7	13	-31
6448m1	25792e1	14508h1	40300a1	78988f1	20956h1	49972a1

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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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