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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 355740.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.ba1 | 355740ba3 | \([0, -1, 0, -1786605, -848369850]\) | \(189123395584/16078125\) | \(53616657277895250000\) | \([2]\) | \(11197440\) | \(2.5271\) | |
| 355740.ba2 | 355740ba1 | \([0, -1, 0, -363645, 84309282]\) | \(1594753024/4725\) | \(15756731934728400\) | \([2]\) | \(3732480\) | \(1.9778\) | \(\Gamma_0(N)\)-optimal |
| 355740.ba3 | 355740ba2 | \([0, -1, 0, -215420, 153500712]\) | \(-20720464/178605\) | \(-9529671474123736320\) | \([2]\) | \(7464960\) | \(2.3244\) | |
| 355740.ba4 | 355740ba4 | \([0, -1, 0, 1919020, -3912180600]\) | \(14647977776/132355125\) | \(-7061957163386139168000\) | \([2]\) | \(22394880\) | \(2.8737\) |
Rank
sage: E.rank()
The elliptic curves in class 355740.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 355740.ba do not have complex multiplication.Modular form 355740.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
