Properties

Label 301180.a
Number of curves 4
Conductor 301180
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("301180.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 301180.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
301180.a1 301180a4 [0, 1, 0, -9720356, -11667879356] [2] 11197440  
301180.a2 301180a3 [0, 1, 0, -609661, -181115100] [2] 5598720  
301180.a3 301180a2 [0, 1, 0, -137356, -11118156] [2] 3732480  
301180.a4 301180a1 [0, 1, 0, -62061, 5808160] [2] 1866240 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301180.a have rank \(2\).

Modular form 301180.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.