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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 10890.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10890.o1 | 10890bb1 | \([1, -1, 0, -96399, 11654253]\) | \(-76711450249/851840\) | \(-1100124074712960\) | \([]\) | \(100800\) | \(1.7011\) | \(\Gamma_0(N)\)-optimal |
10890.o2 | 10890bb2 | \([1, -1, 0, 322866, 60205140]\) | \(2882081488391/2883584000\) | \(-3724056371920896000\) | \([]\) | \(302400\) | \(2.2504\) |
Rank
sage: E.rank()
The elliptic curves in class 10890.o have rank \(0\).
Complex multiplication
The elliptic curves in class 10890.o do not have complex multiplication.Modular form 10890.2.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.