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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 171600.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 171600.k1 | 171600hb4 | \([0, -1, 0, -641521408, -6253886494688]\) | \(912446049969377120252018/17177299425\) | \(549673581600000000\) | \([2]\) | \(33030144\) | \(3.3921\) | |
| 171600.k2 | 171600hb3 | \([0, -1, 0, -43671408, -79238894688]\) | \(287849398425814280018/81784533026485575\) | \(2617105056847538400000000\) | \([2]\) | \(33030144\) | \(3.3921\) | |
| 171600.k3 | 171600hb2 | \([0, -1, 0, -40096408, -97700194688]\) | \(445574312599094932036/61129333175625\) | \(978069330810000000000\) | \([2, 2]\) | \(16515072\) | \(3.0455\) | |
| 171600.k4 | 171600hb1 | \([0, -1, 0, -2283908, -1807694688]\) | \(-329381898333928144/162600887109375\) | \(-650403548437500000000\) | \([2]\) | \(8257536\) | \(2.6989\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 171600.k have rank \(0\).
Complex multiplication
The elliptic curves in class 171600.k do not have complex multiplication.Modular form 171600.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
