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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 155526.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.cx1 | 155526p2 | \([1, 0, 0, -74600, -8142912]\) | \(-6329617441/279936\) | \(-2030588156532096\) | \([]\) | \(1034880\) | \(1.7022\) | |
155526.cx2 | 155526p1 | \([1, 0, 0, -540, 11094]\) | \(-2401/6\) | \(-43522551366\) | \([]\) | \(147840\) | \(0.72927\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 155526.cx do not have complex multiplication.Modular form 155526.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.