Cremona's table of elliptic curves

9310 = 2 · 5 · 7² · 19

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	9310f	Isogeny class
Conductor	9310	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	108864	Modular degree for the optimal curve
Δ	-65034161281250000 = -1 · 24 · 59 · 78 · 192	Discriminant
Eigenvalues	2+  1 5- 7+  0 -4  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-270163,55401406]	[a1,a2,a3,a4,a6]
Generators	[347:1688:1]	Generators of the group modulo torsion
j	-378281142378601/11281250000	j-invariant
L	3.9073876569868	L(r)(E,1)/r!
Ω	0.34740452880316	Real period
R	0.93728092493211	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	74480ca1 83790dn1 46550bt1 9310a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9310f1

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	-4	0	-	9	9	-10	2	-9	-1	0	-12	0	11	-7	0	2	-10	9	3	-10

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Quadratic twists for elliptic curve 9310f1

-4	-3	5	-7
74480ca1	83790dn1	46550bt1	9310a1

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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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