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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 46410.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.bu1 | 46410bt4 | \([1, 1, 1, -3041226, -2011438101]\) | \(3110783631788320625094049/54601964252545027500\) | \(54601964252545027500\) | \([2]\) | \(2949120\) | \(2.5837\) | |
| 46410.bu2 | 46410bt2 | \([1, 1, 1, -388206, 45183003]\) | \(6470092838549419174369/2856011241889587600\) | \(2856011241889587600\) | \([2, 2]\) | \(1474560\) | \(2.2371\) | |
| 46410.bu3 | 46410bt1 | \([1, 1, 1, -329886, 72756699]\) | \(3970228012584527217889/2128880199962880\) | \(2128880199962880\) | \([2]\) | \(737280\) | \(1.8905\) | \(\Gamma_0(N)\)-optimal |
| 46410.bu4 | 46410bt3 | \([1, 1, 1, 1331694, 338253963]\) | \(261178257936835392203231/200410397162293188780\) | \(-200410397162293188780\) | \([2]\) | \(2949120\) | \(2.5837\) |
Rank
sage: E.rank()
The elliptic curves in class 46410.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 46410.bu do not have complex multiplication.Modular form 46410.2.a.bu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
