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SageMath
E = EllipticCurve("ih1")
E.isogeny_class()
Elliptic curves in class 277440.ih
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277440.ih1 | 277440ih7 | \([0, 1, 0, -2098741505, 37006346101503]\) | \(161572377633716256481/914742821250\) | \(5788052479063239229440000\) | \([4]\) | \(113246208\) | \(3.9431\) | |
| 277440.ih2 | 277440ih4 | \([0, 1, 0, -402473345, -3107939428737]\) | \(1139466686381936641/4080\) | \(25816277062778880\) | \([2]\) | \(28311552\) | \(3.2499\) | |
| 277440.ih3 | 277440ih5 | \([0, 1, 0, -133541505, 556209541503]\) | \(41623544884956481/2962701562500\) | \(18746550096036249600000000\) | \([2, 2]\) | \(56623104\) | \(3.5965\) | |
| 277440.ih4 | 277440ih3 | \([0, 1, 0, -26634625, -42533130625]\) | \(330240275458561/67652010000\) | \(428069371081835151360000\) | \([2, 2]\) | \(28311552\) | \(3.2499\) | |
| 277440.ih5 | 277440ih2 | \([0, 1, 0, -25154945, -48566377857]\) | \(278202094583041/16646400\) | \(105330410416137830400\) | \([2, 2]\) | \(14155776\) | \(2.9033\) | |
| 277440.ih6 | 277440ih1 | \([0, 1, 0, -1480065, -852024705]\) | \(-56667352321/16711680\) | \(-105743470849142292480\) | \([2]\) | \(7077888\) | \(2.5568\) | \(\Gamma_0(N)\)-optimal |
| 277440.ih7 | 277440ih6 | \([0, 1, 0, 56597375, -255124305025]\) | \(3168685387909439/6278181696900\) | \(-39725313269028837418598400\) | \([2]\) | \(56623104\) | \(3.5965\) | |
| 277440.ih8 | 277440ih8 | \([0, 1, 0, 121148415, 2427314507775]\) | \(31077313442863199/420227050781250\) | \(-2658994601040000000000000000\) | \([2]\) | \(113246208\) | \(3.9431\) |
Rank
sage: E.rank()
The elliptic curves in class 277440.ih have rank \(0\).
Complex multiplication
The elliptic curves in class 277440.ih do not have complex multiplication.Modular form 277440.2.a.ih
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
