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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 10647.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10647.b1 | 10647i2 | \([0, 0, 1, -97803849, -372290571468]\) | \(-13383627864961024/151263\) | \(-1169365855331754171\) | \([]\) | \(1248000\) | \(3.0349\) | |
| 10647.b2 | 10647i1 | \([0, 0, 1, 72501, -85675860]\) | \(5451776/413343\) | \(-3195422480979441531\) | \([]\) | \(249600\) | \(2.2302\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10647.b have rank \(0\).
Complex multiplication
The elliptic curves in class 10647.b do not have complex multiplication.Modular form 10647.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
