Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1470.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.p1 1470o1 \([1, 0, 0, -736, 2876]\) \(1092727/540\) \(21790947780\) \([2]\) \(1344\) \(0.67682\) \(\Gamma_0(N)\)-optimal
1470.p2 1470o2 \([1, 0, 0, 2694, 22770]\) \(53582633/36450\) \(-1470888975150\) \([2]\) \(2688\) \(1.0234\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1470.p do not have complex multiplication.

Modular form 1470.2.a.p

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