Cremona's table of elliptic curves

31117 = 29² · 37

Field	Data	Notes
Atkin-Lehner	29- 37-	Signs for the Atkin-Lehner involutions
Class	31117g	Isogeny class
Conductor	31117	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	889952	Modular degree for the optimal curve
Δ	-19860282840964661 = -1 · 299 · 372	Discriminant
Eigenvalues	1  1 -3 -4  3 -5 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9538640,11338285807]	[a1,a2,a3,a4,a6]
Generators	[223205:-87276:125]	Generators of the group modulo torsion
j	-6616084455917/1369	j-invariant
L	3.3792207778618	L(r)(E,1)/r!
Ω	0.30487892575971	Real period
R	2.7709530672228	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31117f1	Quadratic twists by: 29

Hecke Eigenvalues for elliptic curve 31117g1

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
1	1	-3	-4	3	-5	-4	0	0	-	-1	-	4	1	9	-1	10	10	10	-2	-14	5	-6	-12	16

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Quadratic twists for elliptic curve 31117g1

29
31117f1

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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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