Properties

Label 30345.i
Number of curves 4
Conductor 30345
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30345.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30345.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.i1 30345v4 [1, 0, 0, -293341, 47165426] [2] 442368  
30345.i2 30345v2 [1, 0, 0, -98266, -11240029] [2, 2] 221184  
30345.i3 30345v1 [1, 0, 0, -96821, -11603880] [2] 110592 \(\Gamma_0(N)\)-optimal
30345.i4 30345v3 [1, 0, 0, 73689, -46353240] [2] 442368  

Rank

sage: E.rank()
 

The elliptic curves in class 30345.i have rank \(0\).

Modular form 30345.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - q^{7} + 3q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 2q^{13} + q^{14} - q^{15} - q^{16} - q^{18} + 8q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.