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Properties

Label 327810.bt
Number of curves $2$
Conductor $327810$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 327810.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327810.bt1 327810bt2 \([1, 1, 1, -11086251, 20633154219]\) \(-1280824409818832580001/822726139895701410\) \(-96792907632589375185090\) \([]\) \(52898832\) \(3.1119\)  
327810.bt2 327810bt1 \([1, 1, 1, -333201, -82653201]\) \(-34773983355859201/4877010000000\) \(-573775349490000000\) \([]\) \(7556976\) \(2.1389\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 327810.bt have rank \(0\).

Complex multiplication

The elliptic curves in class 327810.bt do not have complex multiplication.

Modular form 327810.2.a.bt

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.