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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 181300.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 181300.x1 | 181300y2 | \([0, 1, 0, -14726133, 21746175863]\) | \(750484394082304/578125\) | \(272063312500000000\) | \([]\) | \(3919104\) | \(2.6533\) | |
| 181300.x2 | 181300y1 | \([0, 1, 0, -222133, 15557863]\) | \(2575826944/1266325\) | \(595927479700000000\) | \([]\) | \(1306368\) | \(2.1040\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 181300.x have rank \(1\).
Complex multiplication
The elliptic curves in class 181300.x do not have complex multiplication.Modular form 181300.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
