Cremona's table of elliptic curves

385 = 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	5- 7- 11+	Signs for the Atkin-Lehner involutions
Class	385b	Isogeny class
Conductor	385	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-21175 = -1 · 52 · 7 · 112	Discriminant
Eigenvalues	-1 -2 5- 7- 11+  4 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,0,7]	[a1,a2,a3,a4,a6]
Generators	[-1:3:1]	Generators of the group modulo torsion
j	-1/21175	j-invariant
L	1.0141520787526	L(r)(E,1)/r!
Ω	3.0431080850734	Real period
R	0.33326193168329	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	6160l1 24640p1 3465j1 1925c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 385b1

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	-8	0	-6	-6	-6	0	-4	-6	10	-14	12	12	-12	-8	8	-16	-14	-2

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Quadratic twists for elliptic curve 385b1

-4	8	-3	5	-7	-11	13	17
6160l1	24640p1	3465j1	1925c1	2695b1	4235e1	65065e1	111265b1

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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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