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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 28314.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28314.o1 | 28314c2 | \([1, -1, 0, -405312, -73390960]\) | \(211176358875/55294096\) | \(1928084954187897648\) | \([2]\) | \(368640\) | \(2.2174\) | |
| 28314.o2 | 28314c1 | \([1, -1, 0, -143952, 20123648]\) | \(9460870875/475904\) | \(16594598852612352\) | \([2]\) | \(184320\) | \(1.8709\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28314.o have rank \(0\).
Complex multiplication
The elliptic curves in class 28314.o do not have complex multiplication.Modular form 28314.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
