Properties

Label 28224dy
Number of curves $2$
Conductor $28224$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dy1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 28224dy have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 4 T + 29 T^{2}\) 1.29.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 28224dy do not have complex multiplication.

Modular form 28224.2.a.dy

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{5} - 6 q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 28224dy

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.ba1 28224dy1 \([0, 0, 0, -1176, 13720]\) \(55296/7\) \(22769316864\) \([2]\) \(24576\) \(0.71661\) \(\Gamma_0(N)\)-optimal
28224.ba2 28224dy2 \([0, 0, 0, 1764, 71344]\) \(11664/49\) \(-2550163488768\) \([2]\) \(49152\) \(1.0632\)