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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 47610.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47610.bz1 | 47610bm4 | \([1, -1, 1, -115157, 3960631]\) | \(57960603/31250\) | \(91055950099593750\) | \([2]\) | \(608256\) | \(1.9453\) | |
| 47610.bz2 | 47610bm2 | \([1, -1, 1, -67547, -6739981]\) | \(8527173507/200\) | \(799393800600\) | \([2]\) | \(202752\) | \(1.3960\) | |
| 47610.bz3 | 47610bm1 | \([1, -1, 1, -4067, -112669]\) | \(-1860867/320\) | \(-1279030080960\) | \([2]\) | \(101376\) | \(1.0494\) | \(\Gamma_0(N)\)-optimal |
| 47610.bz4 | 47610bm3 | \([1, -1, 1, 27673, 475579]\) | \(804357/500\) | \(-1456895201593500\) | \([2]\) | \(304128\) | \(1.5987\) |
Rank
sage: E.rank()
The elliptic curves in class 47610.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 47610.bz do not have complex multiplication.Modular form 47610.2.a.bz
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
