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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 63063.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63063.v1 | 63063o4 | \([1, -1, 0, -4372818, -3518481835]\) | \(107818231938348177/4463459\) | \(382813564672539\) | \([2]\) | \(933888\) | \(2.2845\) | |
| 63063.v2 | 63063o3 | \([1, -1, 0, -443508, 21418991]\) | \(112489728522417/62811265517\) | \(5387078598494149557\) | \([2]\) | \(933888\) | \(2.2845\) | |
| 63063.v3 | 63063o2 | \([1, -1, 0, -273723, -54746560]\) | \(26444947540257/169338169\) | \(14523477892372449\) | \([2, 2]\) | \(466944\) | \(1.9379\) | |
| 63063.v4 | 63063o1 | \([1, -1, 0, -6918, -1865809]\) | \(-426957777/17320303\) | \(-1485495202854663\) | \([2]\) | \(233472\) | \(1.5913\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63063.v have rank \(0\).
Complex multiplication
The elliptic curves in class 63063.v do not have complex multiplication.Modular form 63063.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
