Cremona's table of elliptic curves

113715 = 3² · 5 · 7 · 19²

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 19-	Signs for the Atkin-Lehner involutions
Class	113715m	Isogeny class
Conductor	113715	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	22807137420585 = 36 · 5 · 7 · 197	Discriminant
Eigenvalues	1 3- 5+ 7+  4  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-46095,-3790720]	[a1,a2,a3,a4,a6]
Generators	[60000192:17183204792:729]	Generators of the group modulo torsion
j	315821241/665	j-invariant
L	8.3224493067533	L(r)(E,1)/r!
Ω	0.32586716255998	Real period
R	12.769696199805	Regulator
r	1	Rank of the group of rational points
S	0.99999999663397	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12635c1 5985i1	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 113715m1

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	-	+	+	4	2	-2	-	8	6	8	6	6	4	-8	-6	-12	-2	-4	-12	-6	-12	4	-10	-2

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Quadratic twists for elliptic curve 113715m1

-3	-19
12635c1	5985i1

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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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