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SageMath
E = EllipticCurve("rz1")
E.isogeny_class()
Elliptic curves in class 244800.rz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244800.rz1 | 244800rz4 | \([0, 0, 0, -24275138700, -1455762872234000]\) | \(1059623036730633329075378/154307373046875\) | \(230379673500000000000000000\) | \([2]\) | \(330301440\) | \(4.4670\) | |
| 244800.rz2 | 244800rz3 | \([0, 0, 0, -2822090700, 21762561094000]\) | \(1664865424893526702418/826424127435466125\) | \(1233844610868131440896000000000\) | \([2]\) | \(330301440\) | \(4.4670\) | |
| 244800.rz3 | 244800rz2 | \([0, 0, 0, -1521590700, -22607897906000]\) | \(521902963282042184836/6241849278890625\) | \(4659515519294736000000000000\) | \([2, 2]\) | \(165150720\) | \(4.1204\) | |
| 244800.rz4 | 244800rz1 | \([0, 0, 0, -18212700, -908139854000]\) | \(-3579968623693264/1906997690433375\) | \(-355891536979438176000000000\) | \([2]\) | \(82575360\) | \(3.7738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244800.rz have rank \(0\).
Complex multiplication
The elliptic curves in class 244800.rz do not have complex multiplication.Modular form 244800.2.a.rz
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.
