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SageMath
E = EllipticCurve("ui1")
E.isogeny_class()
Elliptic curves in class 235200.ui
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.ui1 | 235200ui3 | \([0, 1, 0, -992820033, 11689060608063]\) | \(898353183174324196/29899176238575\) | \(3602030781739120819200000000\) | \([2]\) | \(141557760\) | \(4.0605\) | |
| 235200.ui2 | 235200ui2 | \([0, 1, 0, -152470033, -471644241937]\) | \(13015144447800784/4341909875625\) | \(130770266869095840000000000\) | \([2, 2]\) | \(70778880\) | \(3.7139\) | |
| 235200.ui3 | 235200ui1 | \([0, 1, 0, -137157533, -618200179437]\) | \(151591373397612544/32558203125\) | \(61287040631250000000000\) | \([2]\) | \(35389440\) | \(3.3673\) | \(\Gamma_0(N)\)-optimal |
| 235200.ui4 | 235200ui4 | \([0, 1, 0, 442879967, -3252524091937]\) | \(79743193254623804/84085819746075\) | \(-10130035309881321139200000000\) | \([2]\) | \(141557760\) | \(4.0605\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.ui have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.ui do not have complex multiplication.Modular form 235200.2.a.ui
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
