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SageMath
E = EllipticCurve("jm1")
E.isogeny_class()
Elliptic curves in class 244800.jm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244800.jm1 | 244800jm4 | \([0, 0, 0, -1046700, -403326000]\) | \(84944038338/2088025\) | \(3117404620800000000\) | \([2]\) | \(3145728\) | \(2.3325\) | |
| 244800.jm2 | 244800jm2 | \([0, 0, 0, -146700, 12474000]\) | \(467720676/180625\) | \(134835840000000000\) | \([2, 2]\) | \(1572864\) | \(1.9859\) | |
| 244800.jm3 | 244800jm1 | \([0, 0, 0, -128700, 17766000]\) | \(1263257424/425\) | \(79315200000000\) | \([2]\) | \(786432\) | \(1.6393\) | \(\Gamma_0(N)\)-optimal |
| 244800.jm4 | 244800jm3 | \([0, 0, 0, 465300, 89586000]\) | \(7462174302/6640625\) | \(-9914400000000000000\) | \([2]\) | \(3145728\) | \(2.3325\) |
Rank
sage: E.rank()
The elliptic curves in class 244800.jm have rank \(0\).
Complex multiplication
The elliptic curves in class 244800.jm do not have complex multiplication.Modular form 244800.2.a.jm
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
