Cremona's table of elliptic curves

11715 = 3 · 5 · 11 · 71

Field	Data	Notes
Atkin-Lehner	3+ 5+ 11- 71-	Signs for the Atkin-Lehner involutions
Class	11715c	Isogeny class
Conductor	11715	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1216	Modular degree for the optimal curve
Δ	128865 = 3 · 5 · 112 · 71	Discriminant
Eigenvalues	1 3+ 5+ -4 11-  2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-18,-33]	[a1,a2,a3,a4,a6]
Generators	[14:45:1]	Generators of the group modulo torsion
j	702595369/128865	j-invariant
L	3.2886934446916	L(r)(E,1)/r!
Ω	2.330459405758	Real period
R	2.8223563444753	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	35145k1 58575u1 128865f1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 11715c1

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	0	0	-4	0	0	-2	-6	-2	12	6	4	0	-4	-	8	8	4	-14	10

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Quadratic twists for elliptic curve 11715c1

-3	5	-11
35145k1	58575u1	128865f1

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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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