Cremona's table of elliptic curves

34656 = 2⁵ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 3- 19-	Signs for the Atkin-Lehner involutions
Class	34656q	Isogeny class
Conductor	34656	Conductor
∏ cp	26	Product of Tamagawa factors cp
deg	29952	Modular degree for the optimal curve
Δ	-36835238592 = -1 · 26 · 313 · 192	Discriminant
Eigenvalues	2+ 3-  2 -1  0  5 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1602,-26892]	[a1,a2,a3,a4,a6]
Generators	[72:486:1]	Generators of the group modulo torsion
j	-19692240832/1594323	j-invariant
L	8.152995241641	L(r)(E,1)/r!
Ω	0.37555378482325	Real period
R	0.83497158791969	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	34656h1 69312cs1 103968ce1 34656v1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 34656q1

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	-1	0	5	-6	-	0	2	9	3	-12	-9	-10	12	-14	-7	1	-12	5	17	6	-2	-2

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Quadratic twists for elliptic curve 34656q1

-4	8	-3	-19
34656h1	69312cs1	103968ce1	34656v1

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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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