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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 159120.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.cz1 | 159120h1 | \([0, 0, 0, -2547, 22194]\) | \(611960049/282880\) | \(844675153920\) | \([2]\) | \(196608\) | \(0.98318\) | \(\Gamma_0(N)\)-optimal |
159120.cz2 | 159120h2 | \([0, 0, 0, 8973, 167346]\) | \(26757728271/19536400\) | \(-58335377817600\) | \([2]\) | \(393216\) | \(1.3298\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.cz have rank \(0\).
Complex multiplication
The elliptic curves in class 159120.cz do not have complex multiplication.Modular form 159120.2.a.cz
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.