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SageMath
E = EllipticCurve("bgj1")
E.isogeny_class()
Elliptic curves in class 705600.bgj
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.bgj1 | \([0, 0, 0, -18654300, -12428262000]\) | \(1210991472/588245\) | \(348720711650922240000000\) | \([2]\) | \(63700992\) | \(3.2109\) |
| 705600.bgj2 | \([0, 0, 0, -15346800, -23124717000]\) | \(10788913152/8575\) | \(317712018632400000000\) | \([2]\) | \(31850496\) | \(2.8643\) |
| 705600.bgj3 | \([0, 0, 0, -9834300, 11869858000]\) | \(129348709488/6125\) | \(4980788064000000000\) | \([2]\) | \(21233664\) | \(2.6616\) |
| 705600.bgj4 | \([0, 0, 0, -646800, 164983000]\) | \(588791808/109375\) | \(5558915250000000000\) | \([2]\) | \(10616832\) | \(2.3150\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bgj have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.bgj do not have complex multiplication.Modular form 705600.2.a.bgj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
