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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 32400.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32400.cv1 | 32400bq4 | \([0, 0, 0, -3877875, 2939267250]\) | \(-189613868625/128\) | \(-4353564672000000\) | \([]\) | \(435456\) | \(2.3165\) | |
| 32400.cv2 | 32400bq3 | \([0, 0, 0, -37875, 5763250]\) | \(-1159088625/2097152\) | \(-10871635968000000\) | \([]\) | \(145152\) | \(1.7672\) | |
| 32400.cv3 | 32400bq1 | \([0, 0, 0, -1875, -32750]\) | \(-140625/8\) | \(-41472000000\) | \([]\) | \(20736\) | \(0.79428\) | \(\Gamma_0(N)\)-optimal |
| 32400.cv4 | 32400bq2 | \([0, 0, 0, 10125, -60750]\) | \(3375/2\) | \(-68024448000000\) | \([]\) | \(62208\) | \(1.3436\) |
Rank
sage: E.rank()
The elliptic curves in class 32400.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 32400.cv do not have complex multiplication.Modular form 32400.2.a.cv
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
