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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8820f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8820.z2 | 8820f1 | \([0, 0, 0, -5292, 83349]\) | \(442368/175\) | \(6483918747600\) | \([2]\) | \(13824\) | \(1.1568\) | \(\Gamma_0(N)\)-optimal |
| 8820.z1 | 8820f2 | \([0, 0, 0, -38367, -2833866]\) | \(10536048/245\) | \(145239779946240\) | \([2]\) | \(27648\) | \(1.5033\) |
Rank
sage: E.rank()
The elliptic curves in class 8820f have rank \(0\).
Complex multiplication
The elliptic curves in class 8820f do not have complex multiplication.Modular form 8820.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
