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Properties

Label 39270.r
Number of curves $2$
Conductor $39270$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 39270.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39270.r1 39270p2 \([1, 1, 0, -1787, 9231]\) \(631650797177401/322548111270\) \(322548111270\) \([2]\) \(67584\) \(0.90062\)  
39270.r2 39270p1 \([1, 1, 0, -1437, 20361]\) \(328523283207001/332616900\) \(332616900\) \([2]\) \(33792\) \(0.55405\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 39270.r have rank \(1\).

Complex multiplication

The elliptic curves in class 39270.r do not have complex multiplication.

Modular form 39270.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + q^{11} - q^{12} + q^{14} - q^{15} + q^{16} - q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.