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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 13680bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13680.bb4 | 13680bx1 | \([0, 0, 0, 529413, -889851094]\) | \(5495662324535111/117739817533440\) | \(-351569211317771304960\) | \([2]\) | \(430080\) | \(2.6227\) | \(\Gamma_0(N)\)-optimal |
| 13680.bb3 | 13680bx2 | \([0, 0, 0, -11267067, -13788122326]\) | \(52974743974734147769/3152005008998400\) | \(9411836524789078425600\) | \([2, 2]\) | \(860160\) | \(2.9693\) | |
| 13680.bb1 | 13680bx3 | \([0, 0, 0, -177615867, -911106819286]\) | \(207530301091125281552569/805586668007040\) | \(2405468901282333327360\) | \([2]\) | \(1720320\) | \(3.3159\) | |
| 13680.bb2 | 13680bx4 | \([0, 0, 0, -33661947, 58041215786]\) | \(1412712966892699019449/330160465517040000\) | \(985853867466433167360000\) | \([4]\) | \(1720320\) | \(3.3159\) |
Rank
sage: E.rank()
The elliptic curves in class 13680bx have rank \(1\).
Complex multiplication
The elliptic curves in class 13680bx do not have complex multiplication.Modular form 13680.2.a.bx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
