Properties

Label 27380d
Number of curves 4
Conductor 27380
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("27380.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27380d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27380.c3 27380d1 [0, 1, 0, -1825, 20028] [2] 25920 \(\Gamma_0(N)\)-optimal
27380.c4 27380d2 [0, 1, 0, 5020, 140500] [2] 51840  
27380.c1 27380d3 [0, 1, 0, -56585, -5198600] [2] 77760  
27380.c2 27380d4 [0, 1, 0, -49740, -6496412] [2] 155520  

Rank

sage: E.rank()
 

The elliptic curves in class 27380d have rank \(1\).

Modular form 27380.2.a.c

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.