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SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 106560fs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.ei3 | 106560fs1 | \([0, 0, 0, -43212, -1890416]\) | \(46694890801/18944000\) | \(3620254777344000\) | \([2]\) | \(442368\) | \(1.6832\) | \(\Gamma_0(N)\)-optimal |
| 106560.ei4 | 106560fs2 | \([0, 0, 0, 141108, -13760624]\) | \(1625964918479/1369000000\) | \(-261619974144000000\) | \([2]\) | \(884736\) | \(2.0298\) | |
| 106560.ei1 | 106560fs3 | \([0, 0, 0, -3038412, -2038534256]\) | \(16232905099479601/4052240\) | \(774395123466240\) | \([2]\) | \(1327104\) | \(2.2325\) | |
| 106560.ei2 | 106560fs4 | \([0, 0, 0, -3026892, -2054759024]\) | \(-16048965315233521/256572640900\) | \(-49031795236169318400\) | \([2]\) | \(2654208\) | \(2.5791\) |
Rank
sage: E.rank()
The elliptic curves in class 106560fs have rank \(0\).
Complex multiplication
The elliptic curves in class 106560fs do not have complex multiplication.Modular form 106560.2.a.fs
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
