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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 141570da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.cc3 | 141570da1 | \([1, -1, 0, -14724, 670720]\) | \(273359449/9360\) | \(12088140189840\) | \([2]\) | \(368640\) | \(1.2821\) | \(\Gamma_0(N)\)-optimal |
| 141570.cc2 | 141570da2 | \([1, -1, 0, -36504, -1755572]\) | \(4165509529/1368900\) | \(1767890502764100\) | \([2, 2]\) | \(737280\) | \(1.6287\) | |
| 141570.cc4 | 141570da3 | \([1, -1, 0, 105066, -12146810]\) | \(99317171591/106616250\) | \(-137691471849896250\) | \([2]\) | \(1474560\) | \(1.9753\) | |
| 141570.cc1 | 141570da4 | \([1, -1, 0, -526554, -146908382]\) | \(12501706118329/2570490\) | \(3319705499634810\) | \([2]\) | \(1474560\) | \(1.9753\) |
Rank
sage: E.rank()
The elliptic curves in class 141570da have rank \(1\).
Complex multiplication
The elliptic curves in class 141570da do not have complex multiplication.Modular form 141570.2.a.da
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.
