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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 39600.dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.dr1 | 39600bx4 | \([0, 0, 0, -3688875, 2727020250]\) | \(4406910829875/7744\) | \(9755209728000000\) | \([2]\) | \(663552\) | \(2.3272\) | |
| 39600.dr2 | 39600bx3 | \([0, 0, 0, -232875, 41708250]\) | \(1108717875/45056\) | \(56757583872000000\) | \([2]\) | \(331776\) | \(1.9807\) | |
| 39600.dr3 | 39600bx2 | \([0, 0, 0, -58875, 1374250]\) | \(13060888875/7086244\) | \(12245029632000000\) | \([2]\) | \(221184\) | \(1.7779\) | |
| 39600.dr4 | 39600bx1 | \([0, 0, 0, -34875, -2489750]\) | \(2714704875/21296\) | \(36799488000000\) | \([2]\) | \(110592\) | \(1.4314\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.dr have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.dr do not have complex multiplication.Modular form 39600.2.a.dr
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.
