Cremona's table of elliptic curves

1365 = 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	3+ 5- 7- 13-	Signs for the Atkin-Lehner involutions
Class	1365b	Isogeny class
Conductor	1365	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	184878500625 = 36 · 54 · 74 · 132	Discriminant
Eigenvalues	-1 3+ 5- 7-  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2975,57692]	[a1,a2,a3,a4,a6]
j	2912015927948401/184878500625	j-invariant
L	0.99320564608121	L(r)(E,1)/r!
Ω	0.99320564608121	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	21840ch2 87360cl2 4095i2 6825h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1365b2

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

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Quadratic twists for elliptic curve 1365b2

-4	8	-3	5	-7	13
21840ch2	87360cl2	4095i2	6825h2	9555q2	17745d2

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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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