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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 5550w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.x2 | 5550w1 | \([1, 1, 1, -30013, -231469]\) | \(306163065625/175056768\) | \(1709538750000000\) | \([]\) | \(45360\) | \(1.6127\) | \(\Gamma_0(N)\)-optimal |
5550.x1 | 5550w2 | \([1, 1, 1, -1764388, -902800219]\) | \(62202232222815625/232783872\) | \(2273280000000000\) | \([]\) | \(136080\) | \(2.1620\) |
Rank
sage: E.rank()
The elliptic curves in class 5550w have rank \(0\).
Complex multiplication
The elliptic curves in class 5550w do not have complex multiplication.Modular form 5550.2.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.