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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 35280dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.el2 | 35280dg1 | \([0, 0, 0, -82467, 9103906]\) | \(4767078987/6860\) | \(89255722106880\) | \([2]\) | \(110592\) | \(1.5793\) | \(\Gamma_0(N)\)-optimal |
| 35280.el3 | 35280dg2 | \([0, 0, 0, -58947, 14405314]\) | \(-1740992427/5882450\) | \(-76536781706649600\) | \([2]\) | \(221184\) | \(1.9259\) | |
| 35280.el1 | 35280dg3 | \([0, 0, 0, -329427, -63771246]\) | \(416832723/56000\) | \(531162623803392000\) | \([2]\) | \(331776\) | \(2.1286\) | |
| 35280.el4 | 35280dg4 | \([0, 0, 0, 517293, -337600494]\) | \(1613964717/6125000\) | \(-58095911978496000000\) | \([2]\) | \(663552\) | \(2.4752\) |
Rank
sage: E.rank()
The elliptic curves in class 35280dg have rank \(0\).
Complex multiplication
The elliptic curves in class 35280dg do not have complex multiplication.Modular form 35280.2.a.dg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
