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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 97020.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.w1 | 97020c1 | \([0, 0, 0, -110103, 14170702]\) | \(-3704530032/33275\) | \(-1325885782636800\) | \([3]\) | \(580608\) | \(1.7250\) | \(\Gamma_0(N)\)-optimal |
| 97020.w2 | 97020c2 | \([0, 0, 0, 342657, 74810358]\) | \(153174672/171875\) | \(-4992617435652000000\) | \([]\) | \(1741824\) | \(2.2743\) |
Rank
sage: E.rank()
The elliptic curves in class 97020.w have rank \(1\).
Complex multiplication
The elliptic curves in class 97020.w do not have complex multiplication.Modular form 97020.2.a.w
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.
