Cremona's table of elliptic curves

4805 = 5 · 31²

Field	Data	Notes
Atkin-Lehner	5+ 31+	Signs for the Atkin-Lehner involutions
Class	4805a	Isogeny class
Conductor	4805	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	65100	Modular degree for the optimal curve
Δ	66632112300078125 = 57 · 318	Discriminant
Eigenvalues	2  2 5+ -2  1  0 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-188676,29059741]	[a1,a2,a3,a4,a6]
Generators	[-6614760:42723953:13824]	Generators of the group modulo torsion
j	870928384/78125	j-invariant
L	8.5192424979194	L(r)(E,1)/r!
Ω	0.33909800376616	Real period
R	8.3744152656962	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	76880m1 43245h1 24025b1 4805d1	Quadratic twists by: -4 -3 5 -31

Hecke Eigenvalues for elliptic curve 4805a1

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
2	2	+	-2	1	0	-2	-8	-4	-3	+	8	-3	6	2	-12	5	1	8	15	2	-9	-4	-7	-12

---

Quadratic twists for elliptic curve 4805a1

-4	-3	5	-31
76880m1	43245h1	24025b1	4805d1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations