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)
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.