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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 153072e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 153072.j1 | 153072e1 | \([0, 0, 0, -164791587, 814281945122]\) | \(-165745346665991446425889/10662541623558144\) | \(-31838178687278641053696\) | \([]\) | \(18966528\) | \(3.3754\) | \(\Gamma_0(N)\)-optimal |
| 153072.j2 | 153072e2 | \([0, 0, 0, 1133230173, -23401988315998]\) | \(53900230693869615719525471/110424476261224735356024\) | \(-329725719324396880177321967616\) | \([]\) | \(132765696\) | \(4.3484\) |
Rank
sage: E.rank()
The elliptic curves in class 153072e have rank \(0\).
Complex multiplication
The elliptic curves in class 153072e do not have complex multiplication.Modular form 153072.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
