Properties

Label 30345b
Number of curves 4
Conductor 30345
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("30345.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30345b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.t3 30345b1 [1, 1, 0, -728, 6867] [2] 20480 \(\Gamma_0(N)\)-optimal
30345.t2 30345b2 [1, 1, 0, -2173, -30992] [2, 2] 40960  
30345.t4 30345b3 [1, 1, 0, 5052, -185607] [2] 81920  
30345.t1 30345b4 [1, 1, 0, -32518, -2270453] [2] 81920  

Rank

sage: E.rank()
 

The elliptic curves in class 30345b have rank \(1\).

Modular form 30345.2.a.t

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - q^{7} - 3q^{8} + q^{9} - q^{10} + q^{12} - 6q^{13} - q^{14} + q^{15} - q^{16} + q^{18} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.