Cremona's table of elliptic curves

34680 = 2³ · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	34680w	Isogeny class
Conductor	34680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	24054048000 = 28 · 32 · 53 · 174	Discriminant
Eigenvalues	2+ 3- 5+ -4  1  4 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7321,-243445]	[a1,a2,a3,a4,a6]
Generators	[-49:6:1]	Generators of the group modulo torsion
j	2029825024/1125	j-invariant
L	5.6374088777413	L(r)(E,1)/r!
Ω	0.51613873935611	Real period
R	1.3652842849905	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360o1 104040dc1 34680m1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 34680w1

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
+	-	+	-4	1	4	-	-1	-2	-1	0	2	-5	2	6	-2	-1	5	-12	-3	4	-11	10	11	-6

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Quadratic twists for elliptic curve 34680w1

-4	-3	17
69360o1	104040dc1	34680m1

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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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