Properties

Label 28900c
Number of curves 2
Conductor 28900
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28900.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28900c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28900.k2 28900c1 [0, 1, 0, 3372, -18892] [] 20736 \(\Gamma_0(N)\)-optimal
28900.k1 28900c2 [0, 1, 0, -54428, -5082172] [] 62208  

Rank

sage: E.rank()
 

The elliptic curves in class 28900c have rank \(0\).

Modular form 28900.2.a.k

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} - 2q^{9} + q^{13} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.