Properties

Label 30345.u
Number of curves 2
Conductor 30345
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30345.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30345.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.u1 30345a2 [1, 1, 0, -361520943, -2343460232862] [2] 11612160  
30345.u2 30345a1 [1, 1, 0, 33505932, -189536694237] [2] 5806080 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 30345.2.a.u

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.