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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 234416bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234416.bj3 | 234416bj1 | \([0, 1, 0, 12709163, 18689024899]\) | \(471114356703100928/585612268875179\) | \(-282200874274389746364416\) | \([]\) | \(26873856\) | \(3.1858\) | \(\Gamma_0(N)\)-optimal |
| 234416.bj2 | 234416bj2 | \([0, 1, 0, -125086677, -838297753021]\) | \(-449167881463536812032/369990050199923699\) | \(-178294617767816492087914496\) | \([]\) | \(80621568\) | \(3.7351\) | |
| 234416.bj1 | 234416bj3 | \([0, 1, 0, -11626452917, -482527996090141]\) | \(-360675992659311050823073792/56219378022244619\) | \(-27091573165830378212274176\) | \([]\) | \(241864704\) | \(4.2844\) |
Rank
sage: E.rank()
The elliptic curves in class 234416bj have rank \(0\).
Complex multiplication
The elliptic curves in class 234416bj do not have complex multiplication.Modular form 234416.2.a.bj
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
