Cremona's table of elliptic curves

3458 = 2 · 7 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2+ 7- 13- 19+	Signs for the Atkin-Lehner involutions
Class	3458b	Isogeny class
Conductor	3458	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1040	Modular degree for the optimal curve
Δ	-269115392 = -1 · 213 · 7 · 13 · 192	Discriminant
Eigenvalues	2+  1  0 7- -1 13-  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-486,4152]	[a1,a2,a3,a4,a6]
Generators	[12:3:1]	Generators of the group modulo torsion
j	-12657482097625/269115392	j-invariant
L	3.0560399171315	L(r)(E,1)/r!
Ω	1.7418355241398	Real period
R	0.8772469830757	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27664m1 110656q1 31122bc1 86450y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3458b1

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
+	1	0	-	-1	-	2	+	3	-8	-7	3	-3	0	7	6	0	-5	-3	-6	-5	-13	2	-10	3

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Quadratic twists for elliptic curve 3458b1

-4	8	-3	5	-7	13	-19
27664m1	110656q1	31122bc1	86450y1	24206c1	44954q1	65702w1

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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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