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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 24336ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24336.k4 | 24336ce1 | \([0, 0, 0, 1179789, -204211150]\) | \(5735339/3888\) | \(-123112996892103868416\) | \([2]\) | \(599040\) | \(2.5436\) | \(\Gamma_0(N)\)-optimal |
| 24336.k3 | 24336ce2 | \([0, 0, 0, -5147571, -1701264526]\) | \(476379541/236196\) | \(7479114561195310006272\) | \([2]\) | \(1198080\) | \(2.8902\) | |
| 24336.k2 | 24336ce3 | \([0, 0, 0, -107967171, 432069951170]\) | \(-4395631034341/3145728\) | \(-99609053880505174327296\) | \([2]\) | \(2995200\) | \(3.3484\) | |
| 24336.k1 | 24336ce4 | \([0, 0, 0, -1727771331, 27642512113346]\) | \(18013780041269221/9216\) | \(291823400040542502912\) | \([2]\) | \(5990400\) | \(3.6949\) |
Rank
sage: E.rank()
The elliptic curves in class 24336ce have rank \(0\).
Complex multiplication
The elliptic curves in class 24336ce do not have complex multiplication.Modular form 24336.2.a.ce
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
