Cremona's table of elliptic curves

2254 = 2 · 7² · 23

Field	Data	Notes
Atkin-Lehner	2+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	2254b	Isogeny class
Conductor	2254	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-85388232412 = -1 · 22 · 79 · 232	Discriminant
Eigenvalues	2+  0  2 7- -4 -4  8  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-401,-14295]	[a1,a2,a3,a4,a6]
Generators	[53:307:1]	Generators of the group modulo torsion
j	-60698457/725788	j-invariant
L	2.4632903753012	L(r)(E,1)/r!
Ω	0.45942579238178	Real period
R	2.6808359654025	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	18032p1 72128l1 20286cf1 56350bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2254b1

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

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Quadratic twists for elliptic curve 2254b1

-4	8	-3	5	-7	-23
18032p1	72128l1	20286cf1	56350bh1	322a1	51842c1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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