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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 28392bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28392.x3 | 28392bc1 | \([0, 1, 0, -1239, -17094]\) | \(2725888/21\) | \(1621807824\) | \([2]\) | \(18432\) | \(0.59629\) | \(\Gamma_0(N)\)-optimal |
| 28392.x2 | 28392bc2 | \([0, 1, 0, -2084, 8256]\) | \(810448/441\) | \(544927428864\) | \([2, 2]\) | \(36864\) | \(0.94286\) | |
| 28392.x4 | 28392bc3 | \([0, 1, 0, 8056, 73152]\) | \(11696828/7203\) | \(-35601925352448\) | \([2]\) | \(73728\) | \(1.2894\) | |
| 28392.x1 | 28392bc4 | \([0, 1, 0, -25744, 1579280]\) | \(381775972/567\) | \(2802483919872\) | \([2]\) | \(73728\) | \(1.2894\) |
Rank
sage: E.rank()
The elliptic curves in class 28392bc have rank \(0\).
Complex multiplication
The elliptic curves in class 28392bc do not have complex multiplication.Modular form 28392.2.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 Cremona 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 Cremona labels.
