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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 76440.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.cx1 | 76440bh4 | \([0, 1, 0, -285000, -58638672]\) | \(10625310339698/3855735\) | \(929020655646720\) | \([2]\) | \(589824\) | \(1.8406\) | |
| 76440.cx2 | 76440bh3 | \([0, 1, 0, -147800, 21376368]\) | \(1481943889298/34543665\) | \(8323128614062080\) | \([2]\) | \(589824\) | \(1.8406\) | |
| 76440.cx3 | 76440bh2 | \([0, 1, 0, -20400, -638352]\) | \(7793764996/3080025\) | \(371058545894400\) | \([2, 2]\) | \(294912\) | \(1.4940\) | |
| 76440.cx4 | 76440bh1 | \([0, 1, 0, 4100, -69952]\) | \(253012016/219375\) | \(-6607167840000\) | \([2]\) | \(147456\) | \(1.1475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76440.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 76440.cx do not have complex multiplication.Modular form 76440.2.a.cx
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.
