Cremona's table of elliptic curves

7215 = 3 · 5 · 13 · 37

Field	Data	Notes
Atkin-Lehner	3- 5+ 13+ 37+	Signs for the Atkin-Lehner involutions
Class	7215f	Isogeny class
Conductor	7215	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	27000192155625 = 312 · 54 · 133 · 37	Discriminant
Eigenvalues	1 3- 5+  4  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7769,-84049]	[a1,a2,a3,a4,a6]
j	51848800828831369/27000192155625	j-invariant
L	3.2308604536204	L(r)(E,1)/r!
Ω	0.53847674227006	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	115440bh1 21645m1 36075g1 93795bc1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7215f1

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	-	+	4	0	+	2	-4	4	2	0	+	-2	-4	8	6	-12	14	-8	12	14	12	-12	-10	14

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Quadratic twists for elliptic curve 7215f1

-4	-3	5	13
115440bh1	21645m1	36075g1	93795bc1

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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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