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SageMath
E = EllipticCurve("oz1")
E.isogeny_class()
Elliptic curves in class 352800.oz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
352800.oz1 | 352800oz1 | \([0, 0, 0, -15107925, 22602328000]\) | \(4446542056384/25725\) | \(2206333462725000000\) | \([2]\) | \(17694720\) | \(2.7102\) | \(\Gamma_0(N)\)-optimal |
352800.oz2 | 352800oz2 | \([0, 0, 0, -14832300, 23466688000]\) | \(-65743598656/5294205\) | \(-29060059304243520000000\) | \([2]\) | \(35389440\) | \(3.0567\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.oz have rank \(0\).
Complex multiplication
The elliptic curves in class 352800.oz do not have complex multiplication.Modular form 352800.2.a.oz
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.