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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 35490.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35490.bo1 | 35490bm8 | \([1, 0, 1, -1090223, 275563628]\) | \(29689921233686449/10380965400750\) | \(50106937225028706750\) | \([2]\) | \(1327104\) | \(2.4815\) | |
| 35490.bo2 | 35490bm5 | \([1, 0, 1, -973613, 369685136]\) | \(21145699168383889/2593080\) | \(12516301881720\) | \([2]\) | \(442368\) | \(1.9322\) | |
| 35490.bo3 | 35490bm6 | \([1, 0, 1, -456473, -115586872]\) | \(2179252305146449/66177562500\) | \(319426454273062500\) | \([2, 2]\) | \(663552\) | \(2.1349\) | |
| 35490.bo4 | 35490bm3 | \([1, 0, 1, -453093, -117426944]\) | \(2131200347946769/2058000\) | \(9933572922000\) | \([2]\) | \(331776\) | \(1.7884\) | |
| 35490.bo5 | 35490bm2 | \([1, 0, 1, -61013, 5740256]\) | \(5203798902289/57153600\) | \(275869510862400\) | \([2, 2]\) | \(221184\) | \(1.5856\) | |
| 35490.bo6 | 35490bm4 | \([1, 0, 1, -13693, 14428208]\) | \(-58818484369/18600435000\) | \(-89780747061915000\) | \([2]\) | \(442368\) | \(1.9322\) | |
| 35490.bo7 | 35490bm1 | \([1, 0, 1, -6933, -78752]\) | \(7633736209/3870720\) | \(18683226132480\) | \([2]\) | \(110592\) | \(1.2390\) | \(\Gamma_0(N)\)-optimal |
| 35490.bo8 | 35490bm7 | \([1, 0, 1, 123197, -388959244]\) | \(42841933504271/13565917968750\) | \(-65480094944824218750\) | \([2]\) | \(1327104\) | \(2.4815\) |
Rank
sage: E.rank()
The elliptic curves in class 35490.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 35490.bo do not have complex multiplication.Modular form 35490.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
