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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 27200.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27200.x1 | 27200bf2 | \([0, -1, 0, -18833, -1024463]\) | \(-115431760/4913\) | \(-31443200000000\) | \([]\) | \(34560\) | \(1.3562\) | |
27200.x2 | 27200bf1 | \([0, -1, 0, 1167, -4463]\) | \(27440/17\) | \(-108800000000\) | \([]\) | \(11520\) | \(0.80685\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27200.x have rank \(0\).
Complex multiplication
The elliptic curves in class 27200.x do not have complex multiplication.Modular form 27200.2.a.x
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.