Properties

Label 8470.t
Number of curves $2$
Conductor $8470$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.t1 8470z1 \([1, 0, 0, -21601, 3963081]\) \(-5200020529/28672000\) \(-6146097836032000\) \([3]\) \(71280\) \(1.7136\) \(\Gamma_0(N)\)-optimal
8470.t2 8470z2 \([1, 0, 0, 191359, -97959575]\) \(3615170357711/21437500000\) \(-4595318511437500000\) \([]\) \(213840\) \(2.2629\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8470.t have rank \(0\).

Complex multiplication

The elliptic curves in class 8470.t do not have complex multiplication.

Modular form 8470.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2q^{3} + q^{4} - q^{5} - 2q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2q^{12} + 2q^{13} + q^{14} + 2q^{15} + q^{16} + 3q^{17} + q^{18} - 7q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.