Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("30345.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30345q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.g2 30345q1 [1, 1, 1, 258446625, -6603697742508] [2] 17233920 \(\Gamma_0(N)\)-optimal
30345.g1 30345q2 [1, 1, 1, -4093169430, -93611649792600] [2] 34467840  

Rank

sage: E.rank()
 

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

Modular form 30345.2.a.g

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

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 Cremona 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 Cremona labels.