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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 114240.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 114240.a1 | 114240q6 | \([0, -1, 0, -1482881, -694531455]\) | \(1375634265228629281/24990412335\) | \(6551086651146240\) | \([2]\) | \(2097152\) | \(2.1610\) | |
| 114240.a2 | 114240q4 | \([0, -1, 0, -366401, 85486401]\) | \(20751759537944401/418359375\) | \(109670400000000\) | \([2]\) | \(1048576\) | \(1.8144\) | |
| 114240.a3 | 114240q3 | \([0, -1, 0, -95681, -10086975]\) | \(369543396484081/45120132225\) | \(11827971941990400\) | \([2, 2]\) | \(1048576\) | \(1.8144\) | |
| 114240.a4 | 114240q2 | \([0, -1, 0, -23681, 1245825]\) | \(5602762882081/716900625\) | \(187931197440000\) | \([2, 2]\) | \(524288\) | \(1.4678\) | |
| 114240.a5 | 114240q1 | \([0, -1, 0, 2239, 100161]\) | \(4733169839/19518975\) | \(-5116782182400\) | \([2]\) | \(262144\) | \(1.1213\) | \(\Gamma_0(N)\)-optimal |
| 114240.a6 | 114240q5 | \([0, -1, 0, 139519, -52093695]\) | \(1145725929069119/5127181719135\) | \(-1344059924580925440\) | \([2]\) | \(2097152\) | \(2.1610\) |
Rank
sage: E.rank()
The elliptic curves in class 114240.a have rank \(2\).
Complex multiplication
The elliptic curves in class 114240.a do not have complex multiplication.Modular form 114240.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
