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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 277200u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.u4 | 277200u1 | \([0, 0, 0, -720075, -203759750]\) | \(885012508801/127733760\) | \(5959546306560000000\) | \([2]\) | \(3538944\) | \(2.3280\) | \(\Gamma_0(N)\)-optimal |
| 277200.u2 | 277200u2 | \([0, 0, 0, -11088075, -14210927750]\) | \(3231355012744321/85377600\) | \(3983377305600000000\) | \([2, 2]\) | \(7077888\) | \(2.6746\) | |
| 277200.u3 | 277200u3 | \([0, 0, 0, -10656075, -15369119750]\) | \(-2868190647517441/527295615000\) | \(-24601504213440000000000\) | \([2]\) | \(14155776\) | \(3.0211\) | |
| 277200.u1 | 277200u4 | \([0, 0, 0, -177408075, -909511487750]\) | \(13235378341603461121/9240\) | \(431101440000000\) | \([2]\) | \(14155776\) | \(3.0211\) |
Rank
sage: E.rank()
The elliptic curves in class 277200u have rank \(1\).
Complex multiplication
The elliptic curves in class 277200u do not have complex multiplication.Modular form 277200.2.a.u
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.
