Cremona's table of elliptic curves

7854 = 2 · 3 · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	7854d	Isogeny class
Conductor	7854	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	67293072 = 24 · 33 · 72 · 11 · 172	Discriminant
Eigenvalues	2+ 3+  0 7- 11+  2 17- -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-280,1648]	[a1,a2,a3,a4,a6]
Generators	[-9:64:1]	Generators of the group modulo torsion
j	2441288319625/67293072	j-invariant
L	2.7368747058849	L(r)(E,1)/r!
Ω	1.9486872640876	Real period
R	0.70223548855756	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	62832bn1 23562bh1 54978r1 86394bm1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854d1

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	-	-2	4	-2	0	-2	-2	-2	6	2	6	4	-12	-8	-12	-4	-8	-2	-18

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Quadratic twists for elliptic curve 7854d1

-4	-3	-7	-11
62832bn1	23562bh1	54978r1	86394bm1

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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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