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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 73920.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.dz1 | 73920fy4 | \([0, -1, 0, -119105, -15779103]\) | \(1425631925916578/270703125\) | \(35481600000000\) | \([2]\) | \(262144\) | \(1.6011\) | |
| 73920.dz2 | 73920fy3 | \([0, -1, 0, -52225, 4465825]\) | \(120186986927618/4332064275\) | \(567812328652800\) | \([2]\) | \(262144\) | \(1.6011\) | |
| 73920.dz3 | 73920fy2 | \([0, -1, 0, -8225, -189375]\) | \(939083699236/300155625\) | \(19670999040000\) | \([2, 2]\) | \(131072\) | \(1.2545\) | |
| 73920.dz4 | 73920fy1 | \([0, -1, 0, 1455, -20943]\) | \(20777545136/23059575\) | \(-377808076800\) | \([2]\) | \(65536\) | \(0.90798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.dz have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.dz do not have complex multiplication.Modular form 73920.2.a.dz
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
