Cremona's table of elliptic curves

31284 = 2² · 3² · 11 · 79

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 79-	Signs for the Atkin-Lehner involutions
Class	31284a	Isogeny class
Conductor	31284	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	460422120837888 = 28 · 39 · 114 · 792	Discriminant
Eigenvalues	2- 3+  0  0 11+ -6  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-897615,327326454]	[a1,a2,a3,a4,a6]
Generators	[438:4266:1]	Generators of the group modulo torsion
j	15873136782246000/91374481	j-invariant
L	4.8592109808479	L(r)(E,1)/r!
Ω	0.46836190767875	Real period
R	1.7291510764011	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	125136j2 31284b2	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 31284a2

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

---

Quadratic twists for elliptic curve 31284a2

-4	-3
125136j2	31284b2

---

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