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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4290.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4290.a1 | 4290e3 | \([1, 1, 0, -838948, -296117492]\) | \(65302476285992806722889/83595669300\) | \(83595669300\) | \([2]\) | \(49152\) | \(1.8039\) | |
| 4290.a2 | 4290e4 | \([1, 1, 0, -65948, -2083692]\) | \(31720417118313330889/16530220800650700\) | \(16530220800650700\) | \([4]\) | \(49152\) | \(1.8039\) | |
| 4290.a3 | 4290e2 | \([1, 1, 0, -52448, -4640592]\) | \(15955978629870426889/18037858410000\) | \(18037858410000\) | \([2, 2]\) | \(24576\) | \(1.4573\) | |
| 4290.a4 | 4290e1 | \([1, 1, 0, -2448, -110592]\) | \(-1623435815226889/4247100000000\) | \(-4247100000000\) | \([2]\) | \(12288\) | \(1.1107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4290.a have rank \(1\).
Complex multiplication
The elliptic curves in class 4290.a do not have complex multiplication.Modular form 4290.2.a.a
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.
