Cremona's table of elliptic curves

31680 = 2⁶ · 3² · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 11+	Signs for the Atkin-Lehner involutions
Class	31680bf	Isogeny class
Conductor	31680	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-8295335568453795840 = -1 · 217 · 310 · 5 · 118	Discriminant
Eigenvalues	2+ 3- 5-  0 11+  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,446388,-77618576]	[a1,a2,a3,a4,a6]
Generators	[14995015:472168467:42875]	Generators of the group modulo torsion
j	102949393183198/86815346805	j-invariant
L	6.5656127126086	L(r)(E,1)/r!
Ω	0.128577436681	Real period
R	12.765872617483	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	31680dv5 3960e6 10560t6	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31680bf5

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
+	-	-	0	+	2	6	4	0	6	-8	-6	-10	4	8	-10	-12	-6	4	0	-14	0	4	6	-14

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Quadratic twists for elliptic curve 31680bf5

-4	8	-3
31680dv5	3960e6	10560t6

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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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