Properties

Label 71478ba
Number of curves 4
Conductor 71478
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("71478.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 71478ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71478.u3 71478ba1 [1, -1, 0, -17937, 876649] [2] 221184 \(\Gamma_0(N)\)-optimal
71478.u4 71478ba2 [1, -1, 0, 14553, 3677287] [2] 442368  
71478.u1 71478ba3 [1, -1, 0, -261612, -51240560] [2] 663552  
71478.u2 71478ba4 [1, -1, 0, -131652, -102262856] [2] 1327104  

Rank

sage: E.rank()
 

The elliptic curves in class 71478ba have rank \(0\).

Modular form 71478.2.a.u

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + 2q^{7} - q^{8} + q^{11} + 4q^{13} - 2q^{14} + q^{16} + 6q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.