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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 386232.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 386232.bc1 | 386232bc3 | \([0, -1, 0, -391112, 78256620]\) | \(1823652903746/328593657\) | \(1192189353141405696\) | \([2]\) | \(6553600\) | \(2.1875\) | |
| 386232.bc2 | 386232bc2 | \([0, -1, 0, -115232, -13887300]\) | \(93280467172/7800849\) | \(14151352171815936\) | \([2, 2]\) | \(3276800\) | \(1.8410\) | |
| 386232.bc3 | 386232bc1 | \([0, -1, 0, -112812, -14546508]\) | \(350104249168/2793\) | \(1266680287488\) | \([2]\) | \(1638400\) | \(1.4944\) | \(\Gamma_0(N)\)-optimal |
| 386232.bc4 | 386232bc4 | \([0, -1, 0, 121928, -63880628]\) | \(55251546334/517244049\) | \(-1876642579846121472\) | \([2]\) | \(6553600\) | \(2.1875\) |
Rank
sage: E.rank()
The elliptic curves in class 386232.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 386232.bc do not have complex multiplication.Modular form 386232.2.a.bc
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
