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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 3300o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3300.m1 | 3300o1 | \([0, 1, 0, -137708, 19623588]\) | \(-2888047810000/35937\) | \(-3593700000000\) | \([3]\) | \(12960\) | \(1.5563\) | \(\Gamma_0(N)\)-optimal |
3300.m2 | 3300o2 | \([0, 1, 0, -62708, 40893588]\) | \(-272709010000/7073843073\) | \(-707384307300000000\) | \([]\) | \(38880\) | \(2.1056\) |
Rank
sage: E.rank()
The elliptic curves in class 3300o have rank \(0\).
Complex multiplication
The elliptic curves in class 3300o 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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.