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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 193200cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.eo1 | 193200cf1 | \([0, 1, 0, -114963408, -298304584812]\) | \(2625564132023811051529/918925030195200000\) | \(58811201932492800000000000\) | \([2]\) | \(41472000\) | \(3.6461\) | \(\Gamma_0(N)\)-optimal |
| 193200.eo2 | 193200cf2 | \([0, 1, 0, 343788592, -2084684872812]\) | \(70213095586874240921591/69970703040000000000\) | \(-4478124994560000000000000000\) | \([2]\) | \(82944000\) | \(3.9927\) |
Rank
sage: E.rank()
The elliptic curves in class 193200cf have rank \(1\).
Complex multiplication
The elliptic curves in class 193200cf do not have complex multiplication.Modular form 193200.2.a.cf
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
