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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 267600.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 267600.ch1 | 267600ch2 | \([0, 1, 0, -90500008, 481317319988]\) | \(-1280824409818832580001/822726139895701410\) | \(-52654472953324890240000000\) | \([]\) | \(80607744\) | \(3.6368\) | |
| 267600.ch2 | 267600ch1 | \([0, 1, 0, -2720008, -1925440012]\) | \(-34773983355859201/4877010000000\) | \(-312128640000000000000\) | \([]\) | \(11515392\) | \(2.6638\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 267600.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 267600.ch do not have complex multiplication.Modular form 267600.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
