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SageMath
E = EllipticCurve("kt1")
E.isogeny_class()
Elliptic curves in class 100800.kt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.kt1 | 100800nj2 | \([0, 0, 0, -23700, -1384000]\) | \(31554496/525\) | \(24494400000000\) | \([2]\) | \(294912\) | \(1.3676\) | |
| 100800.kt2 | 100800nj1 | \([0, 0, 0, -75, -61000]\) | \(-64/2205\) | \(-1607445000000\) | \([2]\) | \(147456\) | \(1.0210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.kt have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.kt do not have complex multiplication.Modular form 100800.2.a.kt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
