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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 59200.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59200.o1 | 59200bf3 | \([0, 1, 0, -8440033, -9440471937]\) | \(16232905099479601/4052240\) | \(16597975040000000\) | \([2]\) | \(1327104\) | \(2.4879\) | |
| 59200.o2 | 59200bf4 | \([0, 1, 0, -8408033, -9515575937]\) | \(-16048965315233521/256572640900\) | \(-1050921537126400000000\) | \([2]\) | \(2654208\) | \(2.8345\) | |
| 59200.o3 | 59200bf1 | \([0, 1, 0, -120033, -8791937]\) | \(46694890801/18944000\) | \(77594624000000000\) | \([2]\) | \(442368\) | \(1.9386\) | \(\Gamma_0(N)\)-optimal |
| 59200.o4 | 59200bf2 | \([0, 1, 0, 391967, -63575937]\) | \(1625964918479/1369000000\) | \(-5607424000000000000\) | \([2]\) | \(884736\) | \(2.2852\) |
Rank
sage: E.rank()
The elliptic curves in class 59200.o have rank \(2\).
Complex multiplication
The elliptic curves in class 59200.o do not have complex multiplication.Modular form 59200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
