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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 187200io
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.y2 | 187200io1 | \([0, 0, 0, 172500, 594110000]\) | \(7604375/2047032\) | \(-152810119987200000000\) | \([]\) | \(4976640\) | \(2.5522\) | \(\Gamma_0(N)\)-optimal |
| 187200.y1 | 187200io2 | \([0, 0, 0, -48427500, 129734030000]\) | \(-168256703745625/30371328\) | \(-2267207486668800000000\) | \([]\) | \(14929920\) | \(3.1015\) |
Rank
sage: E.rank()
The elliptic curves in class 187200io have rank \(1\).
Complex multiplication
The elliptic curves in class 187200io do not have complex multiplication.Modular form 187200.2.a.io
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
