Cremona's table of elliptic curves

34307 = 7 · 13² · 29

Field	Data	Notes
Atkin-Lehner	7+ 13+ 29+	Signs for the Atkin-Lehner involutions
Class	34307d	Isogeny class
Conductor	34307	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240000	Modular degree for the optimal curve
Δ	1406551242740189 = 74 · 134 · 295	Discriminant
Eigenvalues	2 -2  1 7+  2 13+  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-28110,-196023]	[a1,a2,a3,a4,a6]
Generators	[-5356768:7822979:32768]	Generators of the group modulo torsion
j	86009869643776/49247268749	j-invariant
L	8.3322907184512	L(r)(E,1)/r!
Ω	0.39978225443009	Real period
R	10.421036234249	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	34307i1	Quadratic twists by: 13

Hecke Eigenvalues for elliptic curve 34307d1

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	-2	1	+	2	+	6	6	-3	+	6	-8	-12	-2	0	6	-11	10	-5	-9	2	10	-1	-6	2

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Quadratic twists for elliptic curve 34307d1

13
34307i1

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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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