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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 3300.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3300.o1 | 3300q1 | \([0, 1, 0, -1013, -10572]\) | \(57537462272/10673289\) | \(21346578000\) | \([2]\) | \(2304\) | \(0.70022\) | \(\Gamma_0(N)\)-optimal |
3300.o2 | 3300q2 | \([0, 1, 0, 2012, -58972]\) | \(28134667888/64304361\) | \(-2057739552000\) | \([2]\) | \(4608\) | \(1.0468\) |
Rank
sage: E.rank()
The elliptic curves in class 3300.o have rank \(1\).
Complex multiplication
The elliptic curves in class 3300.o do not have complex multiplication.Modular form 3300.2.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.