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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 43758.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43758.o1 | 43758w3 | \([1, -1, 1, -5644355, 5162831939]\) | \(27279667585959979515625/20847389708288\) | \(15197747097341952\) | \([6]\) | \(1410048\) | \(2.4133\) | |
| 43758.o2 | 43758w4 | \([1, -1, 1, -5606915, 5234671811]\) | \(-26740407923656692603625/754628826325811008\) | \(-550124414391516224832\) | \([6]\) | \(2820096\) | \(2.7599\) | |
| 43758.o3 | 43758w1 | \([1, -1, 1, -85100, 3739871]\) | \(93493211839989625/45910522026512\) | \(33468770557327248\) | \([2]\) | \(470016\) | \(1.8640\) | \(\Gamma_0(N)\)-optimal |
| 43758.o4 | 43758w2 | \([1, -1, 1, 310360, 28416575]\) | \(4535182051990706375/3105662922242452\) | \(-2264028270314747508\) | \([2]\) | \(940032\) | \(2.2106\) |
Rank
sage: E.rank()
The elliptic curves in class 43758.o have rank \(1\).
Complex multiplication
The elliptic curves in class 43758.o do not have complex multiplication.Modular form 43758.2.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.
