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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 144150v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144150.er2 | 144150v1 | \([1, 0, 0, 59562, 81770742]\) | \(1685159/209250\) | \(-2901721019519531250\) | \([]\) | \(2764800\) | \(2.2220\) | \(\Gamma_0(N)\)-optimal |
144150.er1 | 144150v2 | \([1, 0, 0, -12553563, 17122102617]\) | \(-15777367606441/3574920\) | \(-49574291551258125000\) | \([]\) | \(8294400\) | \(2.7713\) |
Rank
sage: E.rank()
The elliptic curves in class 144150v have rank \(0\).
Complex multiplication
The elliptic curves in class 144150v do not have complex multiplication.Modular form 144150.2.a.v
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.