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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 224400fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.dx3 | 224400fv1 | \([0, -1, 0, -3311808, 2088410112]\) | \(62768149033310713/6915442583808\) | \(442588325363712000000\) | \([2]\) | \(11796480\) | \(2.6950\) | \(\Gamma_0(N)\)-optimal |
| 224400.dx2 | 224400fv2 | \([0, -1, 0, -12559808, -14890917888]\) | \(3423676911662954233/483711578981136\) | \(30957541054792704000000\) | \([2, 2]\) | \(23592960\) | \(3.0416\) | |
| 224400.dx4 | 224400fv3 | \([0, -1, 0, 20488192, -80061573888]\) | \(14861225463775641287/51859390496937804\) | \(-3319000991804019456000000\) | \([2]\) | \(47185920\) | \(3.3881\) | |
| 224400.dx1 | 224400fv4 | \([0, -1, 0, -193575808, -1036545221888]\) | \(12534210458299016895673/315581882565708\) | \(20197240484205312000000\) | \([2]\) | \(47185920\) | \(3.3881\) |
Rank
sage: E.rank()
The elliptic curves in class 224400fv have rank \(1\).
Complex multiplication
The elliptic curves in class 224400fv do not have complex multiplication.Modular form 224400.2.a.fv
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.
