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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 16900.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16900.o1 | 16900l2 | \([0, -1, 0, -13108, -573288]\) | \(-368484688\) | \(-676000000\) | \([]\) | \(19440\) | \(0.92817\) | |
16900.o2 | 16900l1 | \([0, -1, 0, -108, -1288]\) | \(-208\) | \(-676000000\) | \([]\) | \(6480\) | \(0.37887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16900.o have rank \(0\).
Complex multiplication
The elliptic curves in class 16900.o do not have complex multiplication.Modular form 16900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.