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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 44880cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.cq3 | 44880cr1 | \([0, 1, 0, -838040, 294954900]\) | \(15891267085572193561/3334993530000\) | \(13660133498880000\) | \([2]\) | \(442368\) | \(2.0921\) | \(\Gamma_0(N)\)-optimal |
| 44880.cq2 | 44880cr2 | \([0, 1, 0, -930520, 225742868]\) | \(21754112339458491481/7199734626562500\) | \(29490113030400000000\) | \([2, 2]\) | \(884736\) | \(2.4387\) | |
| 44880.cq4 | 44880cr3 | \([0, 1, 0, 2689800, 1556572500]\) | \(525440531549759128199/559322204589843750\) | \(-2290983750000000000000\) | \([2]\) | \(1769472\) | \(2.7853\) | |
| 44880.cq1 | 44880cr4 | \([0, 1, 0, -6030520, -5533177132]\) | \(5921450764096952391481/200074809015963750\) | \(819506417729387520000\) | \([2]\) | \(1769472\) | \(2.7853\) |
Rank
sage: E.rank()
The elliptic curves in class 44880cr have rank \(0\).
Complex multiplication
The elliptic curves in class 44880cr do not have complex multiplication.Modular form 44880.2.a.cr
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
