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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 28830.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28830.z1 | 28830z4 | \([1, 1, 1, -610687651, 5808416863973]\) | \(28379906689597370652529/1357352437500\) | \(1204655284695572437500\) | \([2]\) | \(8294400\) | \(3.5223\) | |
| 28830.z2 | 28830z3 | \([1, 1, 1, -38104631, 91060892669]\) | \(-6894246873502147249/47925198774000\) | \(-42533790324581687094000\) | \([2]\) | \(4147200\) | \(3.1757\) | |
| 28830.z3 | 28830z2 | \([1, 1, 1, -8198311, 6489356189]\) | \(68663623745397169/19216056254400\) | \(17054320660083072446400\) | \([2]\) | \(2764800\) | \(2.9730\) | |
| 28830.z4 | 28830z1 | \([1, 1, 1, 1334809, 666526493]\) | \(296354077829711/387386634240\) | \(-343807063858200637440\) | \([2]\) | \(1382400\) | \(2.6264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28830.z have rank \(1\).
Complex multiplication
The elliptic curves in class 28830.z do not have complex multiplication.Modular form 28830.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
