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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 250173bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250173.bh3 | 250173bh1 | \([1, -1, 0, -340379928, -2417011415861]\) | \(127164651399625564873/12072019113\) | \(414027366697924270137\) | \([2]\) | \(29675520\) | \(3.3908\) | \(\Gamma_0(N)\)-optimal |
| 250173.bh2 | 250173bh2 | \([1, -1, 0, -341175933, -2405138046080]\) | \(128058892751492323993/1238715547642881\) | \(42483542436250214506884369\) | \([2, 2]\) | \(59351040\) | \(3.7374\) | |
| 250173.bh1 | 250173bh3 | \([1, -1, 0, -602606718, 1786486302139]\) | \(705629104434579771433/368156220977687373\) | \(12626450412152442194107886877\) | \([2]\) | \(118702080\) | \(4.0840\) | |
| 250173.bh4 | 250173bh4 | \([1, -1, 0, -92481228, -5836876280375]\) | \(-2550558824302680073/427664014254832509\) | \(-14667356305186447188248817741\) | \([2]\) | \(118702080\) | \(4.0840\) |
Rank
sage: E.rank()
The elliptic curves in class 250173bh have rank \(0\).
Complex multiplication
The elliptic curves in class 250173bh do not have complex multiplication.Modular form 250173.2.a.bh
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.
