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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 215600bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.cu1 | 215600bp1 | \([0, -1, 0, -20008, 2982512]\) | \(-117649/440\) | \(-3312995840000000\) | \([]\) | \(870912\) | \(1.6637\) | \(\Gamma_0(N)\)-optimal |
| 215600.cu2 | 215600bp2 | \([0, -1, 0, 175992, -70713488]\) | \(80062991/332750\) | \(-2505453104000000000\) | \([]\) | \(2612736\) | \(2.2130\) |
Rank
sage: E.rank()
The elliptic curves in class 215600bp have rank \(0\).
Complex multiplication
The elliptic curves in class 215600bp do not have complex multiplication.Modular form 215600.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
