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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 90168bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90168.t3 | 90168bf1 | \([0, 1, 0, -129279, 15496362]\) | \(618724784128/87947613\) | \(33965465234764752\) | \([2]\) | \(737280\) | \(1.8978\) | \(\Gamma_0(N)\)-optimal |
| 90168.t2 | 90168bf2 | \([0, 1, 0, -546884, -140353824]\) | \(2927363579728/320445801\) | \(1980104353893828864\) | \([2, 2]\) | \(1474560\) | \(2.2444\) | |
| 90168.t4 | 90168bf3 | \([0, 1, 0, 730496, -697291504]\) | \(1744147297148/9513325341\) | \(-235139631961944093696\) | \([4]\) | \(2949120\) | \(2.5910\) | |
| 90168.t1 | 90168bf4 | \([0, 1, 0, -8505944, -9551146368]\) | \(2753580869496292/39328497\) | \(972077373443884032\) | \([2]\) | \(2949120\) | \(2.5910\) |
Rank
sage: E.rank()
The elliptic curves in class 90168bf have rank \(0\).
Complex multiplication
The elliptic curves in class 90168bf do not have complex multiplication.Modular form 90168.2.a.bf
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.
