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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 277440dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277440.dv6 | 277440dv1 | \([0, -1, 0, -1480065, 852024705]\) | \(-56667352321/16711680\) | \(-105743470849142292480\) | \([2]\) | \(7077888\) | \(2.5568\) | \(\Gamma_0(N)\)-optimal |
| 277440.dv5 | 277440dv2 | \([0, -1, 0, -25154945, 48566377857]\) | \(278202094583041/16646400\) | \(105330410416137830400\) | \([2, 2]\) | \(14155776\) | \(2.9033\) | |
| 277440.dv2 | 277440dv3 | \([0, -1, 0, -402473345, 3107939428737]\) | \(1139466686381936641/4080\) | \(25816277062778880\) | \([2]\) | \(28311552\) | \(3.2499\) | |
| 277440.dv4 | 277440dv4 | \([0, -1, 0, -26634625, 42533130625]\) | \(330240275458561/67652010000\) | \(428069371081835151360000\) | \([2, 2]\) | \(28311552\) | \(3.2499\) | |
| 277440.dv7 | 277440dv5 | \([0, -1, 0, 56597375, 255124305025]\) | \(3168685387909439/6278181696900\) | \(-39725313269028837418598400\) | \([2]\) | \(56623104\) | \(3.5965\) | |
| 277440.dv3 | 277440dv6 | \([0, -1, 0, -133541505, -556209541503]\) | \(41623544884956481/2962701562500\) | \(18746550096036249600000000\) | \([2, 2]\) | \(56623104\) | \(3.5965\) | |
| 277440.dv8 | 277440dv7 | \([0, -1, 0, 121148415, -2427314507775]\) | \(31077313442863199/420227050781250\) | \(-2658994601040000000000000000\) | \([4]\) | \(113246208\) | \(3.9431\) | |
| 277440.dv1 | 277440dv8 | \([0, -1, 0, -2098741505, -37006346101503]\) | \(161572377633716256481/914742821250\) | \(5788052479063239229440000\) | \([2]\) | \(113246208\) | \(3.9431\) |
Rank
sage: E.rank()
The elliptic curves in class 277440dv have rank \(0\).
Complex multiplication
The elliptic curves in class 277440dv do not have complex multiplication.Modular form 277440.2.a.dv
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 8 & 8 \\ 8 & 4 & 8 & 2 & 4 & 1 & 2 & 2 \\ 16 & 8 & 16 & 4 & 8 & 2 & 1 & 4 \\ 16 & 8 & 16 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
