Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ex1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.ex1 28224bx2 \([0, 0, 0, -32844, -2292878]\) \(-1713910976512/1594323\) \(-3644851960512\) \([]\) \(49920\) \(1.3333\)  
28224.ex2 28224bx1 \([0, 0, 0, -84, 322]\) \(-28672/3\) \(-6858432\) \([]\) \(3840\) \(0.050792\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.ex

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

Isogeny matrix

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.