Properties

Label 394944.bc
Number of curves $2$
Conductor $394944$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 394944.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
394944.bc1 394944bc2 [0, -1, 0, -1409569, -643635551] [2] 4423680  
394944.bc2 394944bc1 [0, -1, 0, -93089, -8828895] [2] 2211840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 394944.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 394944.bc do not have complex multiplication.

Modular form 394944.2.a.bc

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

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 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.