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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 44616w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44616.m1 | 44616w1 | \([0, 1, 0, -1354760, -607385856]\) | \(55635379958596/24057\) | \(118905389171712\) | \([2]\) | \(790272\) | \(2.0432\) | \(\Gamma_0(N)\)-optimal |
| 44616.m2 | 44616w2 | \([0, 1, 0, -1348000, -613740256]\) | \(-27403349188178/578739249\) | \(-5721013894607751168\) | \([2]\) | \(1580544\) | \(2.3898\) |
Rank
sage: E.rank()
The elliptic curves in class 44616w have rank \(0\).
Complex multiplication
The elliptic curves in class 44616w do not have complex multiplication.Modular form 44616.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
