Cremona's table of elliptic curves

616 = 2³ · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	616a	Isogeny class
Conductor	616	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-42499072 = -1 · 210 · 73 · 112	Discriminant
Eigenvalues	2+  0  0 7+ 11+ -6  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,85,86]	[a1,a2,a3,a4,a6]
Generators	[7:32:1]	Generators of the group modulo torsion
j	66325500/41503	j-invariant
L	2.015785269882	L(r)(E,1)/r!
Ω	1.2592832385463	Real period
R	1.6007401735998	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	1232e1 4928g1 5544p1 15400q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 616a1

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	-2	4	-2	2	2	-8	0	-2	-10	-4	10	4	0	-8	8	-2	-6	2

---

Quadratic twists for elliptic curve 616a1

-4	8	-3	5	-7	-11	13
1232e1	4928g1	5544p1	15400q1	4312b1	6776i1	104104y1

---

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