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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 143055.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 143055.x1 | 143055p1 | \([0, 0, 1, -34217022, -77039233655]\) | \(-251784668965666816/353546875\) | \(-6221112563644171875\) | \([]\) | \(10119168\) | \(2.8785\) | \(\Gamma_0(N)\)-optimal |
| 143055.x2 | 143055p2 | \([0, 0, 1, -25113522, -118924892330]\) | \(-99546392709922816/289614925147075\) | \(-5096147574353003953332075\) | \([]\) | \(30357504\) | \(3.4279\) |
Rank
sage: E.rank()
The elliptic curves in class 143055.x have rank \(1\).
Complex multiplication
The elliptic curves in class 143055.x do not have complex multiplication.Modular form 143055.2.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.
