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SageMath
E = EllipticCurve("fz1")
E.isogeny_class()
Elliptic curves in class 405600fz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 405600.fz1 | 405600fz1 | \([0, 1, 0, -44744158, -115005365812]\) | \(2052450196928704/4317958125\) | \(20841959139373125000000\) | \([2]\) | \(37158912\) | \(3.1677\) | \(\Gamma_0(N)\)-optimal |
| 405600.fz2 | 405600fz2 | \([0, 1, 0, -29344033, -195347817937]\) | \(-9045718037056/48125390625\) | \(-14866692390225000000000000\) | \([2]\) | \(74317824\) | \(3.5143\) |
Rank
sage: E.rank()
The elliptic curves in class 405600fz have rank \(1\).
Complex multiplication
The elliptic curves in class 405600fz do not have complex multiplication.Modular form 405600.2.a.fz
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.
