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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 147294.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147294.p1 | 147294ce2 | \([1, -1, 0, -52047, -2873151]\) | \(181802454625/63252252\) | \(5424900298554492\) | \([2]\) | \(786432\) | \(1.7207\) | |
147294.p2 | 147294ce1 | \([1, -1, 0, 9693, -317115]\) | \(1174241375/1178352\) | \(-101062680212592\) | \([2]\) | \(393216\) | \(1.3741\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147294.p have rank \(0\).
Complex multiplication
The elliptic curves in class 147294.p do not have complex multiplication.Modular form 147294.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.