Properties

Label 21294.a
Number of curves $2$
Conductor $21294$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 21294.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21294.a1 21294w1 \([1, -1, 0, -1033551, -404230527]\) \(-1214950633/196\) \(-19697772749352516\) \([]\) \(449280\) \(2.1361\) \(\Gamma_0(N)\)-optimal
21294.a2 21294w2 \([1, -1, 0, 251694, -1322666604]\) \(17546087/7529536\) \(-756709637939126254656\) \([]\) \(1347840\) \(2.6854\)  

Rank

sage: E.rank()
 

The elliptic curves in class 21294.a have rank \(0\).

Complex multiplication

The elliptic curves in class 21294.a do not have complex multiplication.

Modular form 21294.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{7} - q^{8} + 3 q^{10} - 6 q^{11} + q^{14} + q^{16} + 3 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.