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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 73920f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.t4 | 73920f1 | \([0, -1, 0, -12801, -478719]\) | \(885012508801/127733760\) | \(33484638781440\) | \([2]\) | \(147456\) | \(1.3205\) | \(\Gamma_0(N)\)-optimal |
| 73920.t2 | 73920f2 | \([0, -1, 0, -197121, -33619455]\) | \(3231355012744321/85377600\) | \(22381225574400\) | \([2, 2]\) | \(294912\) | \(1.6671\) | |
| 73920.t3 | 73920f3 | \([0, -1, 0, -189441, -36367359]\) | \(-2868190647517441/527295615000\) | \(-138227381698560000\) | \([2]\) | \(589824\) | \(2.0137\) | |
| 73920.t1 | 73920f4 | \([0, -1, 0, -3153921, -2154827775]\) | \(13235378341603461121/9240\) | \(2422210560\) | \([2]\) | \(589824\) | \(2.0137\) |
Rank
sage: E.rank()
The elliptic curves in class 73920f have rank \(0\).
Complex multiplication
The elliptic curves in class 73920f do not have complex multiplication.Modular form 73920.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
