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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 29988.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29988.t1 | 29988t2 | \([0, 0, 0, -17275440, 27637166788]\) | \(-1272481306550272000/5865429267\) | \(-2628206321530583808\) | \([3]\) | \(881280\) | \(2.7377\) | |
| 29988.t2 | 29988t1 | \([0, 0, 0, -129360, 67984756]\) | \(-534274048000/4146834123\) | \(-1858130950061175552\) | \([]\) | \(293760\) | \(2.1884\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29988.t have rank \(0\).
Complex multiplication
The elliptic curves in class 29988.t do not have complex multiplication.Modular form 29988.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
