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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 26928bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26928.bp4 | 26928bt1 | \([0, 0, 0, -959979, 272356378]\) | \(32765849647039657/8229948198912\) | \(24574493642780049408\) | \([2]\) | \(516096\) | \(2.4306\) | \(\Gamma_0(N)\)-optimal |
| 26928.bp2 | 26928bt2 | \([0, 0, 0, -14277099, 20762077210]\) | \(107784459654566688937/10704361149504\) | \(31963051122640551936\) | \([2, 2]\) | \(1032192\) | \(2.7772\) | |
| 26928.bp3 | 26928bt3 | \([0, 0, 0, -13199979, 24026827930]\) | \(-85183593440646799657/34223681512621656\) | \(-102191365417784062869504\) | \([2]\) | \(2064384\) | \(3.1238\) | |
| 26928.bp1 | 26928bt4 | \([0, 0, 0, -228428139, 1328839459738]\) | \(441453577446719855661097/4354701912\) | \(13003070234001408\) | \([4]\) | \(2064384\) | \(3.1238\) |
Rank
sage: E.rank()
The elliptic curves in class 26928bt have rank \(1\).
Complex multiplication
The elliptic curves in class 26928bt do not have complex multiplication.Modular form 26928.2.a.bt
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
