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SageMath
E = EllipticCurve("mq1")
E.isogeny_class()
Elliptic curves in class 235200.mq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.mq1 | 235200mq4 | \([0, -1, 0, -3333633, -2340460863]\) | \(68017239368/39375\) | \(2371803840000000000\) | \([2]\) | \(4718592\) | \(2.4714\) | |
| 235200.mq2 | 235200mq3 | \([0, -1, 0, -1961633, 1042891137]\) | \(13858588808/229635\) | \(13832359994880000000\) | \([2]\) | \(4718592\) | \(2.4714\) | |
| 235200.mq3 | 235200mq2 | \([0, -1, 0, -246633, -22123863]\) | \(220348864/99225\) | \(747118209600000000\) | \([2, 2]\) | \(2359296\) | \(2.1249\) | |
| 235200.mq4 | 235200mq1 | \([0, -1, 0, 53492, -2615738]\) | \(143877824/108045\) | \(-12711386205000000\) | \([2]\) | \(1179648\) | \(1.7783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.mq have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.mq do not have complex multiplication.Modular form 235200.2.a.mq
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
