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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 49725o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 49725.w1 | 49725o1 | \([1, -1, 0, -13392, -593109]\) | \(23320116793/2873\) | \(32725265625\) | \([2]\) | \(73728\) | \(1.0410\) | \(\Gamma_0(N)\)-optimal |
| 49725.w2 | 49725o2 | \([1, -1, 0, -12267, -697734]\) | \(-17923019113/8254129\) | \(-94019688140625\) | \([2]\) | \(147456\) | \(1.3876\) |
Rank
sage: E.rank()
The elliptic curves in class 49725o have rank \(0\).
Complex multiplication
The elliptic curves in class 49725o do not have complex multiplication.Modular form 49725.2.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 Cremona 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 Cremona labels.
