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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 28224.ge
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.ge1 | 28224ct2 | \([0, 0, 0, -3881388, 2862568240]\) | \(838561807/26244\) | \(202385707572063633408\) | \([2]\) | \(1376256\) | \(2.6715\) | |
| 28224.ge2 | 28224ct1 | \([0, 0, 0, 69972, 151935280]\) | \(4913/1296\) | \(-9994355929484623872\) | \([2]\) | \(688128\) | \(2.3249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.ge have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.ge do not have complex multiplication.Modular form 28224.2.a.ge
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
