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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 206856t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206856.bx3 | 206856t1 | \([0, 0, 0, -680394, -187621603]\) | \(618724784128/87947613\) | \(4951441832617479888\) | \([2]\) | \(3440640\) | \(2.3130\) | \(\Gamma_0(N)\)-optimal |
| 206856.bx2 | 206856t2 | \([0, 0, 0, -2878239, 1692415010]\) | \(2927363579728/320445801\) | \(288657065729893775616\) | \([2, 2]\) | \(6881280\) | \(2.6596\) | |
| 206856.bx1 | 206856t3 | \([0, 0, 0, -44766579, 115285215422]\) | \(2753580869496292/39328497\) | \(141708189131015390208\) | \([2]\) | \(13762560\) | \(3.0061\) | |
| 206856.bx4 | 206856t4 | \([0, 0, 0, 3844581, 8421957830]\) | \(1744147297148/9513325341\) | \(-34278353090567114241024\) | \([2]\) | \(13762560\) | \(3.0061\) |
Rank
sage: E.rank()
The elliptic curves in class 206856t have rank \(1\).
Complex multiplication
The elliptic curves in class 206856t do not have complex multiplication.Modular form 206856.2.a.t
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.
