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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 11025.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11025.o1 | 11025o2 | \([1, -1, 1, -3170, -49318]\) | \(8869743/2401\) | \(953353965375\) | \([2]\) | \(12288\) | \(1.0066\) | |
| 11025.o2 | 11025o1 | \([1, -1, 1, 505, -5218]\) | \(35937/49\) | \(-19456203375\) | \([2]\) | \(6144\) | \(0.66001\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11025.o have rank \(1\).
Complex multiplication
The elliptic curves in class 11025.o do not have complex multiplication.Modular form 11025.2.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.
