Properties

Label 1470n
Number of curves $2$
Conductor $1470$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1470.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1470n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1470.n1 1470n1 [1, 1, 1, -15, -15] [2] 192 \(\Gamma_0(N)\)-optimal
1470.n2 1470n2 [1, 1, 1, 55, -43] [2] 384  

Rank

sage: E.rank()
 

The elliptic curves in class 1470n have rank \(0\).

Modular form 1470.2.a.n

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 2q^{11} - q^{12} + 2q^{13} - q^{15} + q^{16} - 4q^{17} + q^{18} + O(q^{20}) \)

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.