Cremona's table of elliptic curves

5712 = 2⁴ · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 17-	Signs for the Atkin-Lehner involutions
Class	5712b	Isogeny class
Conductor	5712	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	5712 = 24 · 3 · 7 · 17	Discriminant
Eigenvalues	2+ 3+ -2 7+  4  6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-119,-462]	[a1,a2,a3,a4,a6]
j	11745974272/357	j-invariant
L	1.444474580669	L(r)(E,1)/r!
Ω	1.444474580669	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2856c1 22848co1 17136d1 39984p1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5712b1

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

---

Quadratic twists for elliptic curve 5712b1

-4	8	-3	-7	17
2856c1	22848co1	17136d1	39984p1	97104bb1

---

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