Properties

Label 379456bw
Number of curves $2$
Conductor $379456$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 379456bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379456.bw2 379456bw1 \([0, 1, 0, 90776943, -352865827217]\) \(24226243449392/29774625727\) \(-101674161934835907783933952\) \([2]\) \(88473600\) \(3.6764\) \(\Gamma_0(N)\)-optimal
379456.bw1 379456bw2 \([0, 1, 0, -540542977, -3392923769985]\) \(1278763167594532/375974556419\) \(5135500043993349668293246976\) \([2]\) \(176947200\) \(4.0230\)  

Rank

sage: E.rank()
 

The elliptic curves in class 379456bw have rank \(0\).

Complex multiplication

The elliptic curves in class 379456bw do not have complex multiplication.

Modular form 379456.2.a.bw

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