Cremona's table of elliptic curves

61504 = 2⁶ · 31²

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	61504bl	Isogeny class
Conductor	61504	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	184320	Modular degree for the optimal curve
Δ	-28172916849664 = -1 · 210 · 317	Discriminant
Eigenvalues	2-  0 -1 -3 -6 -4  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-65348,-6434856]	[a1,a2,a3,a4,a6]
Generators	[38905:229679:125]	Generators of the group modulo torsion
j	-33958656/31	j-invariant
L	1.765718043892	L(r)(E,1)/r!
Ω	0.14929240361814	Real period
R	5.9136232018208	Regulator
r	1	Rank of the group of rational points
S	1.0000000000614	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	61504j1 15376t1 1984i1	Quadratic twists by: -4 8 -31

Hecke Eigenvalues for elliptic curve 61504bl1

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	-1	-3	-6	-4	0	-5	-4	2	-	-2	-9	-2	-4	12	9	12	-12	-5	14	10	-2	-6	-7

---

Quadratic twists for elliptic curve 61504bl1

-4	8	-31
61504j1	15376t1	1984i1

---

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