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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 67600br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67600.ce3 | 67600br1 | \([0, 1, 0, -8168, -345292]\) | \(-121945/32\) | \(-15816487731200\) | \([]\) | \(103680\) | \(1.2495\) | \(\Gamma_0(N)\)-optimal |
| 67600.ce4 | 67600br2 | \([0, 1, 0, 59432, 2547988]\) | \(46969655/32768\) | \(-16196083436748800\) | \([]\) | \(311040\) | \(1.7988\) | |
| 67600.ce2 | 67600br3 | \([0, 1, 0, -35208, 29993588]\) | \(-25/2\) | \(-386144720000000000\) | \([]\) | \(518400\) | \(2.0542\) | |
| 67600.ce1 | 67600br4 | \([0, 1, 0, -8485208, 9510893588]\) | \(-349938025/8\) | \(-1544578880000000000\) | \([]\) | \(1555200\) | \(2.6035\) |
Rank
sage: E.rank()
The elliptic curves in class 67600br have rank \(0\).
Complex multiplication
The elliptic curves in class 67600br do not have complex multiplication.Modular form 67600.2.a.br
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
