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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 141120eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.hh3 | 141120eq1 | \([0, 0, 0, -16023, -389648]\) | \(82881856/36015\) | \(197687478260160\) | \([2]\) | \(589824\) | \(1.4393\) | \(\Gamma_0(N)\)-optimal |
| 141120.hh2 | 141120eq2 | \([0, 0, 0, -124068, 16551808]\) | \(601211584/11025\) | \(3873060798566400\) | \([2, 2]\) | \(1179648\) | \(1.7858\) | |
| 141120.hh1 | 141120eq3 | \([0, 0, 0, -1976268, 1069342288]\) | \(303735479048/105\) | \(295090346557440\) | \([2]\) | \(2359296\) | \(2.1324\) | |
| 141120.hh4 | 141120eq4 | \([0, 0, 0, -588, 48014512]\) | \(-8/354375\) | \(-995929919631360000\) | \([2]\) | \(2359296\) | \(2.1324\) |
Rank
sage: E.rank()
The elliptic curves in class 141120eq have rank \(0\).
Complex multiplication
The elliptic curves in class 141120eq do not have complex multiplication.Modular form 141120.2.a.eq
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.
