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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 53900w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53900.h2 | 53900w1 | \([0, 1, 0, -61413, -5810057]\) | \(34020720640/456533\) | \(343748165868800\) | \([]\) | \(186624\) | \(1.5960\) | \(\Gamma_0(N)\)-optimal |
53900.h1 | 53900w2 | \([0, 1, 0, -492613, 129974823]\) | \(17557957181440/443889677\) | \(334228330299987200\) | \([]\) | \(559872\) | \(2.1454\) |
Rank
sage: E.rank()
The elliptic curves in class 53900w have rank \(0\).
Complex multiplication
The elliptic curves in class 53900w do not have complex multiplication.Modular form 53900.2.a.w
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.