Properties

Label 327990.bp
Number of curves $2$
Conductor $327990$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bp1 327990bp2 \([1, 0, 0, -716970, -233727228]\) \(68523370149961/243360\) \(144756203398560\) \([2]\) \(3745280\) \(1.9355\)  
327990.bp2 327990bp1 \([1, 0, 0, -44170, -3764188]\) \(-16022066761/998400\) \(-593871603686400\) \([2]\) \(1872640\) \(1.5889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 327990.bp have rank \(0\).

Complex multiplication

The elliptic curves in class 327990.bp do not have complex multiplication.

Modular form 327990.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} - q^{13} - 2q^{14} + q^{15} + q^{16} - 4q^{17} + q^{18} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.