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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 705600.t
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.t1 | \([0, 0, 0, -80629500, -278668978000]\) | \(2640279346000/3087\) | \(67778563974912000000\) | \([2]\) | \(63700992\) | \(3.0884\) |
| 705600.t2 | \([0, 0, 0, -4998000, -4429159000]\) | \(-10061824000/352947\) | \(-484334321737392000000\) | \([2]\) | \(31850496\) | \(2.7418\) |
| 705600.t3 | \([0, 0, 0, -1249500, -172186000]\) | \(9826000/5103\) | \(112042115958528000000\) | \([2]\) | \(21233664\) | \(2.5391\) |
| 705600.t4 | \([0, 0, 0, 294000, -20923000]\) | \(2048000/1323\) | \(-1815497249328000000\) | \([2]\) | \(10616832\) | \(2.1925\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.t have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.t do not have complex multiplication.Modular form 705600.2.a.t
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.
