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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 323400.gx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.gx1 | 323400gx3 | \([0, 1, 0, -6047008, 5721393488]\) | \(12990838708516/144375\) | \(271769190000000000\) | \([2]\) | \(7077888\) | \(2.4988\) | |
| 323400.gx2 | 323400gx2 | \([0, 1, 0, -387508, 84531488]\) | \(13674725584/1334025\) | \(627786828900000000\) | \([2, 2]\) | \(3538944\) | \(2.1522\) | |
| 323400.gx3 | 323400gx1 | \([0, 1, 0, -87383, -8507262]\) | \(2508888064/396165\) | \(11652104021250000\) | \([2]\) | \(1769472\) | \(1.8056\) | \(\Gamma_0(N)\)-optimal |
| 323400.gx4 | 323400gx4 | \([0, 1, 0, 469992, 406951488]\) | \(6099383804/41507235\) | \(-78132555048240000000\) | \([2]\) | \(7077888\) | \(2.4988\) |
Rank
sage: E.rank()
The elliptic curves in class 323400.gx have rank \(0\).
Complex multiplication
The elliptic curves in class 323400.gx do not have complex multiplication.Modular form 323400.2.a.gx
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.
