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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 286110t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.t3 | 286110t1 | \([1, -1, 0, -6895305, -6965891699]\) | \(2060455000819249/517017600\) | \(9097590487782297600\) | \([2]\) | \(10616832\) | \(2.6249\) | \(\Gamma_0(N)\)-optimal |
| 286110.t2 | 286110t2 | \([1, -1, 0, -7727625, -5177901875]\) | \(2900285849172529/1019696040000\) | \(17942864989380008040000\) | \([2, 2]\) | \(21233664\) | \(2.9714\) | |
| 286110.t1 | 286110t3 | \([1, -1, 0, -51944625, 140322558325]\) | \(880895732965860529/26454814115400\) | \(465506522896535626235400\) | \([2]\) | \(42467328\) | \(3.3180\) | |
| 286110.t4 | 286110t4 | \([1, -1, 0, 23172255, -36257001179]\) | \(78200142092480591/77517928125000\) | \(-1364027773024732303125000\) | \([2]\) | \(42467328\) | \(3.3180\) |
Rank
sage: E.rank()
The elliptic curves in class 286110t have rank \(1\).
Complex multiplication
The elliptic curves in class 286110t do not have complex multiplication.Modular form 286110.2.a.t
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.
