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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 203280.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.bo1 | 203280di8 | \([0, -1, 0, -49306025776, -4214003072604224]\) | \(1826870018430810435423307849/7641104625000000000\) | \(55446253365533184000000000000\) | \([2]\) | \(477757440\) | \(4.7243\) | |
| 203280.bo2 | 203280di6 | \([0, -1, 0, -3129483056, -63692354164800]\) | \(467116778179943012100169/28800309694464000000\) | \(208984086293030249693184000000\) | \([2, 2]\) | \(238878720\) | \(4.3778\) | |
| 203280.bo3 | 203280di5 | \([0, -1, 0, -847529536, -833621711360]\) | \(9278380528613437145689/5328033205714065000\) | \(38661881175851068233584640000\) | \([2]\) | \(159252480\) | \(4.1750\) | |
| 203280.bo4 | 203280di3 | \([0, -1, 0, -591929136, 4316120934336]\) | \(3160944030998056790089/720291785342976000\) | \(5226663262347214461075456000\) | \([2]\) | \(119439360\) | \(4.0312\) | |
| 203280.bo5 | 203280di2 | \([0, -1, 0, -555348416, 5017246780416]\) | \(2610383204210122997209/12104550027662400\) | \(87834414086371856410214400\) | \([2, 2]\) | \(79626240\) | \(3.8285\) | |
| 203280.bo6 | 203280di1 | \([0, -1, 0, -554728896, 5029041945600]\) | \(2601656892010848045529/56330588160\) | \(408752427382037544960\) | \([2]\) | \(39813120\) | \(3.4819\) | \(\Gamma_0(N)\)-optimal |
| 203280.bo7 | 203280di4 | \([0, -1, 0, -273079616, 10113214788096]\) | \(-310366976336070130009/5909282337130963560\) | \(-42879607301939474167059087360\) | \([2]\) | \(159252480\) | \(4.1750\) | |
| 203280.bo8 | 203280di7 | \([0, -1, 0, 2446196944, -265964642932800]\) | \(223090928422700449019831/4340371122724101696000\) | \(-31495095118005175601837899776000\) | \([2]\) | \(477757440\) | \(4.7243\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.bo do not have complex multiplication.Modular form 203280.2.a.bo
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 6 & 12 & 12 & 4 \\ 2 & 1 & 6 & 2 & 3 & 6 & 6 & 2 \\ 3 & 6 & 1 & 12 & 2 & 4 & 4 & 12 \\ 4 & 2 & 12 & 1 & 6 & 3 & 12 & 4 \\ 6 & 3 & 2 & 6 & 1 & 2 & 2 & 6 \\ 12 & 6 & 4 & 3 & 2 & 1 & 4 & 12 \\ 12 & 6 & 4 & 12 & 2 & 4 & 1 & 3 \\ 4 & 2 & 12 & 4 & 6 & 12 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
