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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 223080.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223080.cb1 | 223080be3 | \([0, -1, 0, -4336684720, 109923513052300]\) | \(912446049969377120252018/17177299425\) | \(169802841006663321600\) | \([2]\) | \(115605504\) | \(3.8698\) | |
| 223080.cb2 | 223080be4 | \([0, -1, 0, -295218720, 1393057075500]\) | \(287849398425814280018/81784533026485575\) | \(808465039509581438525798400\) | \([2]\) | \(115605504\) | \(3.8698\) | |
| 223080.cb3 | 223080be2 | \([0, -1, 0, -271051720, 1717503883900]\) | \(445574312599094932036/61129333175625\) | \(302141046308971858560000\) | \([2, 2]\) | \(57802752\) | \(3.5232\) | |
| 223080.cb4 | 223080be1 | \([0, -1, 0, -15439220, 31790568900]\) | \(-329381898333928144/162600887109375\) | \(-200919916878723900000000\) | \([4]\) | \(28901376\) | \(3.1767\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 223080.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 223080.cb do not have complex multiplication.Modular form 223080.2.a.cb
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.
