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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 36300.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36300.o1 | 36300x1 | \([0, -1, 0, -3065333, 1703746662]\) | \(57537462272/10673289\) | \(590886954191531250000\) | \([2]\) | \(1382400\) | \(2.7039\) | \(\Gamma_0(N)\)-optimal |
| 36300.o2 | 36300x2 | \([0, -1, 0, 6085292, 9921007912]\) | \(28134667888/64304361\) | \(-56959549038760500000000\) | \([2]\) | \(2764800\) | \(3.0505\) |
Rank
sage: E.rank()
The elliptic curves in class 36300.o have rank \(0\).
Complex multiplication
The elliptic curves in class 36300.o do not have complex multiplication.Modular form 36300.2.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.
