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SageMath
E = EllipticCurve("bcl1")
E.isogeny_class()
Elliptic curves in class 705600.bcl
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.bcl1 | \([0, 0, 0, -164772300, -814091978000]\) | \(5633270409316/14175\) | \(1244912399539200000000\) | \([2]\) | \(75497472\) | \(3.2860\) |
| 705600.bcl2 | \([0, 0, 0, -28944300, 43871758000]\) | \(30534944836/8203125\) | \(720435416400000000000000\) | \([2]\) | \(75497472\) | \(3.2860\) |
| 705600.bcl3 | \([0, 0, 0, -10422300, -12398078000]\) | \(5702413264/275625\) | \(6051657497760000000000\) | \([2, 2]\) | \(37748736\) | \(2.9395\) |
| 705600.bcl4 | \([0, 0, 0, 382200, -750827000]\) | \(4499456/180075\) | \(-247109347825200000000\) | \([2]\) | \(18874368\) | \(2.5929\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bcl have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.bcl do not have complex multiplication.Modular form 705600.2.a.bcl
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.
