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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 38640bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.o4 | 38640bf1 | \([0, -1, 0, -376, -80]\) | \(1439069689/828345\) | \(3392901120\) | \([2]\) | \(22528\) | \(0.51833\) | \(\Gamma_0(N)\)-optimal |
| 38640.o2 | 38640bf2 | \([0, -1, 0, -4296, -106704]\) | \(2141202151369/5832225\) | \(23888793600\) | \([2, 2]\) | \(45056\) | \(0.86491\) | |
| 38640.o3 | 38640bf3 | \([0, -1, 0, -2616, -192720]\) | \(-483551781049/3672913125\) | \(-15044252160000\) | \([2]\) | \(90112\) | \(1.2115\) | |
| 38640.o1 | 38640bf4 | \([0, -1, 0, -68696, -6907344]\) | \(8753151307882969/65205\) | \(267079680\) | \([2]\) | \(90112\) | \(1.2115\) |
Rank
sage: E.rank()
The elliptic curves in class 38640bf have rank \(0\).
Complex multiplication
The elliptic curves in class 38640bf do not have complex multiplication.Modular form 38640.2.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.
