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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 20800.dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20800.dy1 | 20800bn2 | \([0, -1, 0, -18128833, -29703974463]\) | \(-6434774386429585/140608\) | \(-14398259200000000\) | \([]\) | \(1036800\) | \(2.6268\) | |
20800.dy2 | 20800bn1 | \([0, -1, 0, -208833, -46374463]\) | \(-9836106385/3407872\) | \(-348966092800000000\) | \([]\) | \(345600\) | \(2.0775\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20800.dy have rank \(0\).
Complex multiplication
The elliptic curves in class 20800.dy do not have complex multiplication.Modular form 20800.2.a.dy
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.