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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 393129.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 393129.ch1 | 393129ch1 | \([1, -1, 0, -15087, -641888]\) | \(1157625/121\) | \(39697764249033\) | \([2]\) | \(1036800\) | \(1.3444\) | \(\Gamma_0(N)\)-optimal |
| 393129.ch2 | 393129ch2 | \([1, -1, 0, 19398, -3173087]\) | \(2460375/14641\) | \(-4803429474132993\) | \([2]\) | \(2073600\) | \(1.6909\) |
Rank
sage: E.rank()
The elliptic curves in class 393129.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 393129.ch do not have complex multiplication.Modular form 393129.2.a.ch
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.
