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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 14651e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14651.h3 | 14651e1 | \([0, -1, 1, 794323, -292214595]\) | \(471114356703100928/585612268875179\) | \(-68896697820895934171\) | \([]\) | \(373248\) | \(2.4927\) | \(\Gamma_0(N)\)-optimal |
| 14651.h2 | 14651e2 | \([0, -1, 1, -7817917, 13100356870]\) | \(-449167881463536812032/369990050199923699\) | \(-43528959415970823263651\) | \([]\) | \(1119744\) | \(3.0420\) | |
| 14651.h1 | 14651e3 | \([0, -1, 1, -726653307, 7539681602235]\) | \(-360675992659311050823073792/56219378022244619\) | \(-6614153604939057180731\) | \([]\) | \(3359232\) | \(3.5913\) |
Rank
sage: E.rank()
The elliptic curves in class 14651e have rank \(0\).
Complex multiplication
The elliptic curves in class 14651e do not have complex multiplication.Modular form 14651.2.a.e
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.
