Properties

Label 270.c
Number of curves 2
Conductor 270
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("270.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
270.c1 270b2 [1, -1, 1, -1433, -20519] [] 180  
270.c2 270b1 [1, -1, 1, 7, -103] [3] 60 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 270.c have rank \(0\).

Modular form 270.2.a.c

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + 2q^{7} + q^{8} - q^{10} + 3q^{11} + 5q^{13} + 2q^{14} + q^{16} - 3q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.