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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 317900.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317900.w1 | 317900w2 | \([0, 1, 0, -375133, -88563137]\) | \(-5050365927424/171875\) | \(-198687500000000\) | \([]\) | \(2239488\) | \(1.8353\) | |
317900.w2 | 317900w1 | \([0, 1, 0, -1133, -299137]\) | \(-139264/33275\) | \(-38465900000000\) | \([]\) | \(746496\) | \(1.2860\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 317900.w have rank \(0\).
Complex multiplication
The elliptic curves in class 317900.w do not have complex multiplication.Modular form 317900.2.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.