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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 27456cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27456.cc1 | 27456cj1 | \([0, 1, 0, -369561665, -2737533428289]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-6871100656897545990045696\) | \([]\) | \(6773760\) | \(3.6755\) | \(\Gamma_0(N)\)-optimal |
| 27456.cc2 | 27456cj2 | \([0, 1, 0, 1046597695, 171799068860991]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-12823763814067254789530917011456\) | \([]\) | \(47416320\) | \(4.6485\) |
Rank
sage: E.rank()
The elliptic curves in class 27456cj have rank \(1\).
Complex multiplication
The elliptic curves in class 27456cj do not have complex multiplication.Modular form 27456.2.a.cj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
