Cremona's table of elliptic curves

3120 = 2⁴ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	3120g	Isogeny class
Conductor	3120	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	140400000000 = 210 · 33 · 58 · 13	Discriminant
Eigenvalues	2+ 3- 5+  0  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7696,-261820]	[a1,a2,a3,a4,a6]
Generators	[-49:6:1]	Generators of the group modulo torsion
j	49235161015876/137109375	j-invariant
L	3.7826824181239	L(r)(E,1)/r!
Ω	0.50980170159238	Real period
R	2.4733031204804	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1560i4 12480bz3 9360s4 15600a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3120g3

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

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Quadratic twists for elliptic curve 3120g3

-4	8	-3	5	13
1560i4	12480bz3	9360s4	15600a3	40560y4

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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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