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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 333270.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333270.bp1 | 333270bp1 | \([1, -1, 0, -674574, 209365380]\) | \(8493409990827/185150000\) | \(740038810905450000\) | \([2]\) | \(5406720\) | \(2.2171\) | \(\Gamma_0(N)\)-optimal |
| 333270.bp2 | 333270bp2 | \([1, -1, 0, 55446, 638179128]\) | \(4716275733/44023437500\) | \(-175960315093007812500\) | \([2]\) | \(10813440\) | \(2.5636\) |
Rank
sage: E.rank()
The elliptic curves in class 333270.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 333270.bp do not have complex multiplication.Modular form 333270.2.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.
