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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 171600ds
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 171600.h3 | 171600ds1 | \([0, -1, 0, -26408, 1203312]\) | \(31824875809/8785920\) | \(562298880000000\) | \([2]\) | \(663552\) | \(1.5377\) | \(\Gamma_0(N)\)-optimal |
| 171600.h2 | 171600ds2 | \([0, -1, 0, -154408, -22348688]\) | \(6361447449889/294465600\) | \(18845798400000000\) | \([2, 2]\) | \(1327104\) | \(1.8843\) | |
| 171600.h4 | 171600ds3 | \([0, -1, 0, 85592, -85708688]\) | \(1083523132511/50179392120\) | \(-3211481095680000000\) | \([2]\) | \(2654208\) | \(2.2309\) | |
| 171600.h1 | 171600ds4 | \([0, -1, 0, -2442408, -1468364688]\) | \(25176685646263969/57915000\) | \(3706560000000000\) | \([2]\) | \(2654208\) | \(2.2309\) |
Rank
sage: E.rank()
The elliptic curves in class 171600ds have rank \(1\).
Complex multiplication
The elliptic curves in class 171600ds do not have complex multiplication.Modular form 171600.2.a.ds
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
