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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 308550ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308550.ee3 | 308550ee1 | \([1, 0, 1, -158442001, 767480512148]\) | \(15891267085572193561/3334993530000\) | \(92314757390630156250000\) | \([2]\) | \(53084160\) | \(3.4026\) | \(\Gamma_0(N)\)-optimal |
| 308550.ee2 | 308550ee2 | \([1, 0, 1, -175926501, 587634945148]\) | \(21754112339458491481/7199734626562500\) | \(199293266793245141601562500\) | \([2, 2]\) | \(106168320\) | \(3.7492\) | |
| 308550.ee4 | 308550ee3 | \([1, 0, 1, 508540249, 4044192032648]\) | \(525440531549759128199/559322204589843750\) | \(-15482396938834190368652343750\) | \([2]\) | \(212336640\) | \(4.0958\) | |
| 308550.ee1 | 308550ee4 | \([1, 0, 1, -1140145251, -14378968492352]\) | \(5921450764096952391481/200074809015963750\) | \(5538198886486402451777343750\) | \([2]\) | \(212336640\) | \(4.0958\) |
Rank
sage: E.rank()
The elliptic curves in class 308550ee have rank \(1\).
Complex multiplication
The elliptic curves in class 308550ee do not have complex multiplication.Modular form 308550.2.a.ee
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.
