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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 51600.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.ct1 | 51600u4 | \([0, 1, 0, -6192008, -5932620012]\) | \(820480625548035842/5805\) | \(185760000000\) | \([2]\) | \(811008\) | \(2.2167\) | |
| 51600.ct2 | 51600u3 | \([0, 1, 0, -414008, -79128012]\) | \(245245463376482/57692266875\) | \(1846152540000000000\) | \([2]\) | \(811008\) | \(2.2167\) | |
| 51600.ct3 | 51600u2 | \([0, 1, 0, -387008, -92790012]\) | \(400649568576484/33698025\) | \(539168400000000\) | \([2, 2]\) | \(405504\) | \(1.8701\) | |
| 51600.ct4 | 51600u1 | \([0, 1, 0, -22508, -1665012]\) | \(-315278049616/114259815\) | \(-457039260000000\) | \([2]\) | \(202752\) | \(1.5235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51600.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.ct do not have complex multiplication.Modular form 51600.2.a.ct
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.
