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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 283220o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
283220.o1 | 283220o1 | \([0, -1, 0, -287940, 59602600]\) | \(-177953104/125\) | \(-1854537701408000\) | \([]\) | \(1990656\) | \(1.8660\) | \(\Gamma_0(N)\)-optimal |
283220.o2 | 283220o2 | \([0, -1, 0, 278500, 252645352]\) | \(161017136/1953125\) | \(-28977151584500000000\) | \([]\) | \(5971968\) | \(2.4153\) |
Rank
sage: E.rank()
The elliptic curves in class 283220o have rank \(1\).
Complex multiplication
The elliptic curves in class 283220o do not have complex multiplication.Modular form 283220.2.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.