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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 41616cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41616.b1 | 41616cr1 | \([0, 0, 0, -104907, 8302970]\) | \(1771561/612\) | \(44109529637732352\) | \([2]\) | \(442368\) | \(1.8955\) | \(\Gamma_0(N)\)-optimal |
| 41616.b2 | 41616cr2 | \([0, 0, 0, 311253, 57826010]\) | \(46268279/46818\) | \(-3374379017286524928\) | \([2]\) | \(884736\) | \(2.2421\) |
Rank
sage: E.rank()
The elliptic curves in class 41616cr have rank \(1\).
Complex multiplication
The elliptic curves in class 41616cr do not have complex multiplication.Modular form 41616.2.a.cr
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
