Cremona's table of elliptic curves

30345 = 3 · 5 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	30345f	Isogeny class
Conductor	30345	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	470016	Modular degree for the optimal curve
Δ	-5720012105409984375 = -1 · 32 · 56 · 73 · 179	Discriminant
Eigenvalues	-1 3+ 5+ 7- -2 -4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,111259,-114132166]	[a1,a2,a3,a4,a6]
j	1284365503/48234375	j-invariant
L	0.69275139271803	L(r)(E,1)/r!
Ω	0.11545856545316	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	91035bq1 30345bg1	Quadratic twists by: -3 17

Hecke Eigenvalues for elliptic curve 30345f1

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	+	+	-	-2	-4	+	4	-4	0	4	10	-2	4	-2	6	0	10	0	6	6	-10	6	2	2

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Quadratic twists for elliptic curve 30345f1

-3	17
91035bq1	30345bg1

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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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