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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 273600.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.bn1 | 273600bn3 | \([0, 0, 0, -17761586700, 911106819286000]\) | \(207530301091125281552569/805586668007040\) | \(2405468901282333327360000000\) | \([2]\) | \(330301440\) | \(4.4672\) | |
273600.bn2 | 273600bn4 | \([0, 0, 0, -3366194700, -58041215786000]\) | \(1412712966892699019449/330160465517040000\) | \(985853867466433167360000000000\) | \([2]\) | \(330301440\) | \(4.4672\) | |
273600.bn3 | 273600bn2 | \([0, 0, 0, -1126706700, 13788122326000]\) | \(52974743974734147769/3152005008998400\) | \(9411836524789078425600000000\) | \([2, 2]\) | \(165150720\) | \(4.1206\) | |
273600.bn4 | 273600bn1 | \([0, 0, 0, 52941300, 889851094000]\) | \(5495662324535111/117739817533440\) | \(-351569211317771304960000000\) | \([2]\) | \(82575360\) | \(3.7740\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 273600.bn do not have complex multiplication.Modular form 273600.2.a.bn
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.