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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 117117.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.bp1 | 117117ca1 | \([1, -1, 0, -27151227, 54460431000]\) | \(1382084250541230782125/19771083137421\) | \(31665623776974260073\) | \([2]\) | \(6050304\) | \(2.8812\) | \(\Gamma_0(N)\)-optimal |
| 117117.bp2 | 117117ca2 | \([1, -1, 0, -26372592, 57730230819]\) | \(-1266556547153680328125/165777947457789051\) | \(-265512115761711895339263\) | \([2]\) | \(12100608\) | \(3.2277\) |
Rank
sage: E.rank()
The elliptic curves in class 117117.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 117117.bp do not have complex multiplication.Modular form 117117.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
