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	616c	Isogeny class
Conductor	616	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-216832 = -1 · 28 · 7 · 112	Discriminant
Eigenvalues	2+ -2  2 7- 11+  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12,-32]	[a1,a2,a3,a4,a6]
j	-810448/847	j-invariant
L	1.2228749425822	L(r)(E,1)/r!
Ω	1.2228749425822	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1232c1 4928p1 5544y1 15400l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 616c1

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

---

Quadratic twists for elliptic curve 616c1

-4	8	-3	5	-7	-11	13
1232c1	4928p1	5544y1	15400l1	4312d1	6776h1	104104t1

---

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