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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 92400.fo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.fo1 | 92400cc4 | \([0, 1, 0, -123408, 16645188]\) | \(12990838708516/144375\) | \(2310000000000\) | \([2]\) | \(294912\) | \(1.5258\) | |
| 92400.fo2 | 92400cc2 | \([0, 1, 0, -7908, 244188]\) | \(13674725584/1334025\) | \(5336100000000\) | \([2, 2]\) | \(147456\) | \(1.1792\) | |
| 92400.fo3 | 92400cc1 | \([0, 1, 0, -1783, -25312]\) | \(2508888064/396165\) | \(99041250000\) | \([2]\) | \(73728\) | \(0.83266\) | \(\Gamma_0(N)\)-optimal |
| 92400.fo4 | 92400cc3 | \([0, 1, 0, 9592, 1189188]\) | \(6099383804/41507235\) | \(-664115760000000\) | \([4]\) | \(294912\) | \(1.5258\) |
Rank
sage: E.rank()
The elliptic curves in class 92400.fo have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.fo do not have complex multiplication.Modular form 92400.2.a.fo
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 LMFDB 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 LMFDB labels.
