Cremona's table of elliptic curves

3100 = 2² · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 5- 31-	Signs for the Atkin-Lehner involutions
Class	3100f	Isogeny class
Conductor	3100	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	30031250000 = 24 · 59 · 312	Discriminant
Eigenvalues	2-  2 5- -4  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1333,-16338]	[a1,a2,a3,a4,a6]
j	8388608/961	j-invariant
L	2.3878933691295	L(r)(E,1)/r!
Ω	0.79596445637649	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12400ba1 49600bh1 27900t1 3100g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3100f1

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	-	-4	4	-2	-6	4	6	10	-	10	6	2	0	10	-8	10	4	0	6	8	-6	-18	12

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Quadratic twists for elliptic curve 3100f1

-4	8	-3	5	-31
12400ba1	49600bh1	27900t1	3100g1	96100n1

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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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