Cremona's table of elliptic curves

10605 = 3 · 5 · 7 · 101

Field	Data	Notes
Atkin-Lehner	3+ 5- 7+ 101-	Signs for the Atkin-Lehner involutions
Class	10605c	Isogeny class
Conductor	10605	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	51840	Modular degree for the optimal curve
Δ	402734293565625 = 312 · 55 · 74 · 101	Discriminant
Eigenvalues	1 3+ 5- 7+  0 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-18482,48039]	[a1,a2,a3,a4,a6]
Generators	[-62:1011:1]	Generators of the group modulo torsion
j	698244181406954281/402734293565625	j-invariant
L	4.2380107406502	L(r)(E,1)/r!
Ω	0.45328837690232	Real period
R	1.869896055845	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	31815b1 53025r1 74235j1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 10605c1

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

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Quadratic twists for elliptic curve 10605c1

-3	5	-7
31815b1	53025r1	74235j1

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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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