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SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 277200hi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.hi1 | 277200hi1 | \([0, 0, 0, -17982075, -29348689750]\) | \(13782741913468081/701662500\) | \(32736765600000000000\) | \([2]\) | \(13271040\) | \(2.8146\) | \(\Gamma_0(N)\)-optimal |
| 277200.hi2 | 277200hi2 | \([0, 0, 0, -17010075, -32662237750]\) | \(-11666347147400401/3126621093750\) | \(-145875633750000000000000\) | \([2]\) | \(26542080\) | \(3.1612\) |
Rank
sage: E.rank()
The elliptic curves in class 277200hi have rank \(0\).
Complex multiplication
The elliptic curves in class 277200hi do not have complex multiplication.Modular form 277200.2.a.hi
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
