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SageMath
E = EllipticCurve("hy1")
E.isogeny_class()
Elliptic curves in class 705600.hy
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.hy1 | \([0, 0, 0, -1076054700, 13582936514000]\) | \(784478485879202/221484375\) | \(38903512485600000000000000\) | \([2]\) | \(301989888\) | \(3.8913\) |
| 705600.hy2 | \([0, 0, 0, -75866700, 154412426000]\) | \(549871953124/200930625\) | \(17646633263468160000000000\) | \([2, 2]\) | \(150994944\) | \(3.5447\) |
| 705600.hy3 | \([0, 0, 0, -32648700, -70061866000]\) | \(175293437776/4862025\) | \(106751238260486400000000\) | \([2, 2]\) | \(75497472\) | \(3.1982\) |
| 705600.hy4 | \([0, 0, 0, -32428200, -71077489000]\) | \(2748251600896/2205\) | \(3025828748880000000\) | \([2]\) | \(37748736\) | \(2.8516\) |
| 705600.hy5 | \([0, 0, 0, 7041300, -229536286000]\) | \(439608956/259416045\) | \(-22783086494526919680000000\) | \([2]\) | \(150994944\) | \(3.5447\) |
| 705600.hy6 | \([0, 0, 0, 232833300, 1092243026000]\) | \(7947184069438/7533176175\) | \(-1323194981047023974400000000\) | \([2]\) | \(301989888\) | \(3.8913\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.hy have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.hy do not have complex multiplication.Modular form 705600.2.a.hy
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
